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In particular, the control of quantum\u2013optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.<\/jats:p>","DOI":"10.3390\/e26050401","type":"journal-article","created":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T08:59:39Z","timestamp":1714553979000},"page":"401","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1804-3976","authenticated-orcid":false,"given":"Patrick","family":"Adelhardt","sequence":"first","affiliation":[{"name":"Department of Physics, Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91058 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2464-7709","authenticated-orcid":false,"given":"Jan A.","family":"Koziol","sequence":"additional","affiliation":[{"name":"Department of Physics, Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91058 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2638-8827","authenticated-orcid":false,"given":"Anja","family":"Langheld","sequence":"additional","affiliation":[{"name":"Department of Physics, Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91058 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8278-8238","authenticated-orcid":false,"given":"Kai P.","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Department of Physics, Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91058 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1103\/PhysRevB.8.281","article-title":"Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions","volume":"8","author":"Sak","year":"1973","journal-title":"Phys. Rev. B"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4344","DOI":"10.1103\/PhysRevB.15.4344","article-title":"Low-temperature renormalization group for ferromagnets with long-range interactions","volume":"15","author":"Sak","year":"1977","journal-title":"Phys. Rev. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1103\/PhysRevLett.29.917","article-title":"Critical Exponents for Long-Range Interactions","volume":"29","author":"Fisher","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"013001","DOI":"10.1088\/1751-8121\/ab5634","article-title":"One-dimensional quantum many body systems with long-range interactions","volume":"53","author":"Maity","year":"2019","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"035002","DOI":"10.1103\/RevModPhys.95.035002","article-title":"Long-range interacting quantum systems","volume":"95","author":"Defenu","year":"2023","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3174","DOI":"10.1103\/PhysRevB.4.3174","article-title":"Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture","volume":"4","author":"Wilson","year":"1971","journal-title":"Phys. Rev. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3184","DOI":"10.1103\/PhysRevB.4.3184","article-title":"Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior","volume":"4","author":"Wilson","year":"1971","journal-title":"Phys. Rev. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0370-1573(74)90023-4","article-title":"The renormalization group and the epsilon expansion","volume":"12","author":"Wilson","year":"1974","journal-title":"Phys. Rep."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1103\/RevModPhys.55.583","article-title":"The renormalization group and critical phenomena","volume":"55","author":"Wilson","year":"1983","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1103\/RevModPhys.70.653","article-title":"Renormalization group theory: Its basis and formulation in statistical physics","volume":"70","author":"Fisher","year":"1998","journal-title":"Rev. Mod. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"S358","DOI":"10.1103\/RevModPhys.71.S358","article-title":"Scaling, universality, and renormalization: Three pillars of modern critical phenomena","volume":"71","author":"Stanley","year":"1999","journal-title":"Rev. Mod. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1142\/S0129183195000265","article-title":"Monte Carlo method for spin models with long-range interactions","volume":"6","author":"Luijten","year":"1995","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8945","DOI":"10.1103\/PhysRevB.56.8945","article-title":"Classical critical behavior of spin models with long-range interactions","volume":"56","author":"Luijten","year":"1997","journal-title":"Phys. Rev. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"174438","DOI":"10.1103\/PhysRevB.71.174438","article-title":"Finite-size scaling of the correlation length above the upper critical dimension in the five-dimensional Ising model","volume":"71","author":"Jones","year":"2005","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.nuclphysb.2012.07.021","article-title":"Hyperscaling above the upper critical dimension","volume":"865","author":"Berche","year":"2012","journal-title":"Nucl. Phys. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"26005","DOI":"10.1209\/0295-5075\/105\/26005","article-title":"Fisher\u2019s scaling relation above the upper critical dimension","volume":"105","author":"Kenna","year":"2014","journal-title":"EPL (Europhys. Lett.)"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kenna, R., and Berche, B. (2014). A new critical exponent koppa and its logarithmic counterpart koppa-hat. arXiv.","DOI":"10.5488\/CMP.16.23601"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1140\/epjb\/e2014-50683-1","article-title":"Finite-size scaling above the upper critical dimension in Ising models with long-range interactions","volume":"88","author":"Berche","year":"2015","journal-title":"Eur. Phys. J. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"115701","DOI":"10.1103\/PhysRevLett.116.115701","article-title":"Role of Fourier Modes in Finite-Size Scaling above the Upper Critical Dimension","volume":"116","author":"Berche","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"184106","DOI":"10.1103\/PhysRevB.64.184106","article-title":"Phase transitions in the quantum Ising and rotor models with a long-range interaction","volume":"64","author":"Dutta","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"104432","DOI":"10.1103\/PhysRevB.96.104432","article-title":"Criticality and phase diagram of quantum long-range O(N) models","volume":"96","author":"Defenu","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"P12001","DOI":"10.1088\/1742-5468\/2005\/12\/P12001","article-title":"Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains","volume":"2005","author":"Laflorencie","year":"2005","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"267203","DOI":"10.1103\/PhysRevLett.109.267203","article-title":"Entanglement Entropy for the Long-Range Ising Chain in a Transverse Field","volume":"109","author":"Koffel","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"015001","DOI":"10.1088\/1367-2630\/18\/1\/015001","article-title":"Long-range Ising and Kitaev models: Phases, correlations and edge modes","volume":"18","author":"Vodola","year":"2015","journal-title":"New J. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"075156","DOI":"10.1103\/PhysRevB.94.075156","article-title":"Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit","volume":"94","author":"Fey","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"043621","DOI":"10.1103\/PhysRevA.96.043621","article-title":"Fidelity susceptibility study of quantum long-range antiferromagnetic Ising chain","volume":"96","author":"Sun","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"155116","DOI":"10.1103\/PhysRevB.97.155116","article-title":"Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice","volume":"97","author":"Saadatmand","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"023607","DOI":"10.1103\/PhysRevA.98.023607","article-title":"Fidelity and criticality of a quantum Ising chain with long-range interactions","volume":"98","author":"Zhu","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"017203","DOI":"10.1103\/PhysRevLett.122.017203","article-title":"Quantum Criticality of Two-Dimensional Quantum Magnets with Long-Range Interactions","volume":"122","author":"Fey","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"144411","DOI":"10.1103\/PhysRevB.100.144411","article-title":"Quantum criticality of the transverse-field Ising model with long-range interactions on triangular-lattice cylinders","volume":"100","author":"Koziol","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"174424","DOI":"10.1103\/PhysRevB.102.174424","article-title":"Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field","volume":"102","author":"Adelhardt","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"245135","DOI":"10.1103\/PhysRevB.103.245135","article-title":"Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations","volume":"103","author":"Koziol","year":"2021","journal-title":"Phys. Rev. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"76","DOI":"10.21468\/SciPostPhys.11.4.076","article-title":"Finite-temperature critical behavior of long-range quantum Ising models","volume":"11","author":"Heyl","year":"2021","journal-title":"SciPost Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"88","DOI":"10.21468\/SciPostPhys.13.4.088","article-title":"Scaling at quantum phase transitions above the upper critical dimension","volume":"13","author":"Langheld","year":"2022","journal-title":"SciPost Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"87","DOI":"10.21468\/SciPostPhys.15.3.087","article-title":"Continuously varying critical exponents in long-range quantum spin ladders","volume":"15","author":"Adelhardt","year":"2023","journal-title":"SciPost Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1038\/s41535-023-00591-6","article-title":"Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model","volume":"8","author":"Zhao","year":"2023","journal-title":"npj Quantum Mater."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"L081114","DOI":"10.1103\/PhysRevB.109.L081114","article-title":"Quantum criticality and entanglement for the two-dimensional long-range Heisenberg bilayer","volume":"109","author":"Song","year":"2024","journal-title":"Phys. Rev. B"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"033046","DOI":"10.1103\/PhysRevResearch.5.033046","article-title":"Dynamical properties of quantum many-body systems with long-range interactions","volume":"5","author":"Song","year":"2023","journal-title":"Phys. Rev. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"056701","DOI":"10.1103\/PhysRevE.68.056701","article-title":"Stochastic series expansion method for quantum Ising models with arbitrary interactions","volume":"68","author":"Sandvik","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"104412","DOI":"10.1103\/PhysRevB.93.104412","article-title":"Quantum Monte Carlo study of long-range transverse-field Ising models on the triangular lattice","volume":"93","author":"Humeniuk","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Berche, B., Ellis, T., Holovatch, Y., and Kenna, R. (2022). Phase transitions above the upper critical dimension. SciPost Phys. Lect. Notes, 60.","DOI":"10.21468\/SciPostPhysLectNotes.60"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Dauxois, T., Ruffo, S., Arimondo, E., and Wilkens, M. (2002). Dynamics and Thermodynamics of Systems with Long-Range Interactions, Springer.","DOI":"10.1007\/3-540-45835-2"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.physrep.2009.07.001","article-title":"Statistical mechanics and dynamics of solvable models with long-range interactions","volume":"480","author":"Campa","year":"2009","journal-title":"Phys. Rep."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1103\/RevModPhys.82.1887","article-title":"Long range interactions in nanoscale science","volume":"82","author":"French","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1016\/j.physa.2010.02.024","article-title":"Thermodynamics and dynamics of systems with long-range interactions","volume":"389","author":"Bouchet","year":"2010","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"113002","DOI":"10.1103\/PhysRevLett.114.113002","article-title":"Coherent Excitation Transfer in a Spin Chain of Three Rydberg Atoms","volume":"114","author":"Barredo","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1126\/science.aah3778","article-title":"An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays","volume":"354","author":"Barredo","year":"2016","journal-title":"Science"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1038\/nature18274","article-title":"Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models","volume":"534","author":"Labuhn","year":"2016","journal-title":"Nature"},{"key":"ref_49","first-page":"021070","article-title":"Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions","volume":"8","author":"Lienhard","year":"2018","journal-title":"Phys. Rev. X"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"023001","DOI":"10.1088\/2058-9565\/aa9c59","article-title":"Quantum simulation of transverse Ising models with Rydberg atoms","volume":"3","author":"Schauss","year":"2018","journal-title":"Quantum Sci. Technol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1126\/science.aav9105","article-title":"Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms","volume":"365","author":"Lienhard","year":"2019","journal-title":"Science"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1038\/s41567-019-0733-z","article-title":"Many-body physics with individually controlled Rydberg atoms","volume":"16","author":"Browaeys","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1038\/s41586-021-03585-1","article-title":"Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms","volume":"595","author":"Scholl","year":"2021","journal-title":"Nature"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"e2015785118","DOI":"10.1073\/pnas.2015785118","article-title":"Quantum phases of Rydberg atoms on a kagome lattice","volume":"118","author":"Samajdar","year":"2021","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1126\/science.abi8794","article-title":"Probing topological spin liquids on a programmable quantum simulator","volume":"374","author":"Semeghini","year":"2021","journal-title":"Science"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"3108","DOI":"10.1103\/PhysRevLett.81.3108","article-title":"Cold Bosonic Atoms in Optical Lattices","volume":"81","author":"Jaksch","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1038\/415039a","article-title":"Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms","volume":"415","author":"Greiner","year":"2002","journal-title":"Nature"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"170406","DOI":"10.1103\/PhysRevLett.88.170406","article-title":"Quantum Phases of Dipolar Bosons in Optical Lattices","volume":"88","author":"Santos","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1038\/nphys138","article-title":"Ultracold quantum gases in optical lattices","volume":"1","author":"Bloch","year":"2005","journal-title":"Nat. Phys."},{"key":"ref_60","unstructured":"Bloch, I., and Greiner, M. (2005). Advances in Atomic, Molecular, and Optical Physics, Elsevier."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1209\/epl\/i2005-10231-y","article-title":"Density wave and supersolid phases of correlated bosons in an optical lattice","volume":"72","author":"Kovrizhin","year":"2005","journal-title":"Europhys. Lett. (EPL)"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"235301","DOI":"10.1103\/PhysRevLett.98.235301","article-title":"Metastable States of a Gas of Dipolar Bosons in a 2D Optical Lattice","volume":"98","author":"Menotti","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1103\/RevModPhys.80.885","article-title":"Many-body physics with ultracold gases","volume":"80","author":"Bloch","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"125301","DOI":"10.1103\/PhysRevLett.104.125301","article-title":"Quantum Phases of Cold Polar Molecules in 2D Optical Lattices","volume":"104","author":"Trefzger","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1038\/nphys2259","article-title":"Quantum simulations with ultracold quantum gases","volume":"8","author":"Bloch","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"054516","DOI":"10.1103\/PhysRevB.86.054516","article-title":"Quantum phases of hard-core bosons with long-range interactions on a square lattice","volume":"86","author":"Yamamoto","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1126\/science.aac6400","article-title":"Creation of a low-entropy quantum gas of polar molecules in an optical lattice","volume":"350","author":"Moses","year":"2015","journal-title":"Science"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1126\/science.aac9812","article-title":"Extended Bose\u2013Hubbard models with ultracold magnetic atoms","volume":"352","author":"Baier","year":"2016","journal-title":"Science"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1038\/nphys3985","article-title":"New frontiers for quantum gases of polar molecules","volume":"13","author":"Moses","year":"2017","journal-title":"Nat. Phys."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1126\/science.aal3837","article-title":"Quantum simulations with ultracold atoms in optical lattices","volume":"357","author":"Gross","year":"2017","journal-title":"Science"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1038\/s42254-020-0195-3","article-title":"Tools for quantum simulation with ultracold atoms in optical lattices","volume":"2","author":"Fukuhara","year":"2020","journal-title":"Nat. Rev. Phys."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"026401","DOI":"10.1088\/1361-6633\/aca814","article-title":"Dipolar physics: A review of experiments with magnetic quantum gases","volume":"86","author":"Chomaz","year":"2022","journal-title":"Rep. Prog. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1038\/s41586-023-06614-3","article-title":"Dipolar quantum solids emerging in a Hubbard quantum simulator","volume":"622","author":"Su","year":"2023","journal-title":"Nature"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1038\/nphys1032","article-title":"Simulating a quantum magnet with trapped ions","volume":"4","author":"Friedenauer","year":"2008","journal-title":"Nat. Phys."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"120502","DOI":"10.1103\/PhysRevLett.103.120502","article-title":"Entanglement and Tunable Spin-Spin Couplings between Trapped Ions Using Multiple Transverse Modes","volume":"103","author":"Kim","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1038\/nature09071","article-title":"Quantum simulation of frustrated Ising spins with trapped ions","volume":"465","author":"Kim","year":"2010","journal-title":"Nature"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1038\/ncomms1374","article-title":"Onset of a quantum phase transition with a trapped ion quantum simulator","volume":"2","author":"Islam","year":"2011","journal-title":"Nat. Commun."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1038\/nphys2252","article-title":"Quantum simulations with trapped ions","volume":"8","author":"Blatt","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"024401","DOI":"10.1088\/0034-4885\/75\/2\/024401","article-title":"Experimental quantum simulations of many-body physics with trapped ions","volume":"75","author":"Schneider","year":"2012","journal-title":"Rep. Prog. Phys."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1038\/nature10981","article-title":"Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins","volume":"484","author":"Britton","year":"2012","journal-title":"Nature"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1126\/science.1232296","article-title":"Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator","volume":"340","author":"Islam","year":"2013","journal-title":"Science"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1038\/nature13461","article-title":"Quasiparticle engineering and entanglement propagation in a quantum many-body system","volume":"511","author":"Jurcevic","year":"2014","journal-title":"Nature"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1038\/nature13450","article-title":"Non-local propagation of correlations in quantum systems with long-range interactions","volume":"511","author":"Richerme","year":"2014","journal-title":"Nature"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1126\/science.aad9958","article-title":"Quantum spin dynamics and entanglement generation with hundreds of trapped ions","volume":"352","author":"Bohnet","year":"2016","journal-title":"Science"},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Monroe, C., Campbell, W., Duan, L.M., Gong, Z.X., Gorshkov, A., Hess, P., Islam, R., Kim, K., Linke, N., and Pagano, G. (2021). Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys., 93.","DOI":"10.1103\/RevModPhys.93.025001"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1038\/nphoton.2015.57","article-title":"Quantum many-body models with cold atoms coupled to photonic crystals","volume":"9","author":"Douglas","year":"2015","journal-title":"Nat. Photonics"},{"key":"ref_87","first-page":"011002","article-title":"Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED","volume":"8","author":"Vaidya","year":"2018","journal-title":"Phys. Rev. X"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1103\/RevModPhys.71.87","article-title":"Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states)","volume":"71","author":"Dubin","year":"1999","journal-title":"Rev. Mod. Phys."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1143\/PTP.16.569","article-title":"A Lattice Model of Liquid Helium, I","volume":"16","author":"Matsubara","year":"1956","journal-title":"Prog. Theor. Phys."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1103\/PhysRevLett.79.2554","article-title":"Geometrical Frustration in the Ferromagnetic Pyrochlore Ho2Ti2O7","volume":"79","author":"Harris","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"L215","DOI":"10.1088\/0953-8984\/10\/14\/002","article-title":"Frustration in Ising-type spin models on the pyrochlore lattice","volume":"10","author":"Bramwell","year":"1998","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1038\/20619","article-title":"Zero-point entropy in \u2018spin ice\u2019","volume":"399","author":"Ramirez","year":"1999","journal-title":"Nature"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"1854","DOI":"10.1103\/PhysRevLett.83.1854","article-title":"Ising Pyrochlore Magnets: Low-Temperature Properties, \u201cIce Rules,\u201d and Beyond","volume":"83","author":"Siddharthan","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"3430","DOI":"10.1103\/PhysRevLett.84.3430","article-title":"Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets","volume":"84","author":"Gingras","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"067203","DOI":"10.1103\/PhysRevLett.87.067203","article-title":"Long-Range Order at Low Temperatures in Dipolar Spin Ice","volume":"87","author":"Melko","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"R1277","DOI":"10.1088\/0953-8984\/16\/43\/R02","article-title":"Monte Carlo studies of the dipolar spin ice model","volume":"16","author":"Melko","year":"2004","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1126\/science.1064761","article-title":"Spin Ice State in Frustrated Magnetic Pyrochlore Materials","volume":"294","author":"Bramwell","year":"2001","journal-title":"Science"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"097202","DOI":"10.1103\/PhysRevLett.95.097202","article-title":"Finite-Temperature Transitions in Dipolar Spin Ice in a Large Magnetic Field","volume":"95","author":"Ruff","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1126\/science.1177582","article-title":"Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7","volume":"326","author":"Fennell","year":"2009","journal-title":"Science"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1038\/nature06433","article-title":"Magnetic monopoles in spin ice","volume":"451","author":"Castelnovo","year":"2008","journal-title":"Nature"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1038\/nphys1227","article-title":"Signature of magnetic monopole and Dirac string dynamics in spin ice","volume":"5","author":"Jaubert","year":"2009","journal-title":"Nat. Phys."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1103\/PhysRevLett.77.940","article-title":"Quantum Critical Behavior for a Model Magnet","volume":"77","author":"Bitko","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"144411","DOI":"10.1103\/PhysRevB.70.144411","article-title":"Theory of the magnetic phase diagram of LiHoF4","volume":"70","author":"Chakraborty","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1126\/science.1108317","article-title":"Quantum Phase Transition of a Magnet in a Spin Bath","volume":"308","author":"Ronnow","year":"2005","journal-title":"Science"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/320\/1\/012001","article-title":"Collective Phenomena in the LiHoxY1-xF4Quantum Ising Magnet: Recent Progress and Open Questions","volume":"320","author":"Gingras","year":"2011","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"L020407","DOI":"10.1103\/PhysRevB.109.L020407","article-title":"Phase transition in the two-dimensional Heisenberg ferromagnet Fe3GeTe2 with long-range interaction","volume":"109","author":"Tiwari","year":"2024","journal-title":"Phys. Rev. B"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/s41586-018-0631-z","article-title":"Magnetism in two-dimensional van der Waals materials","volume":"563","author":"Burch","year":"2018","journal-title":"Nature"},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"6960","DOI":"10.1021\/acsnano.1c09150","article-title":"The Magnetic Genome of Two-Dimensional van der Waals Materials","volume":"16","author":"Wang","year":"2022","journal-title":"ACS Nano"},{"key":"ref_109","first-page":"031005","article-title":"Prediction of Toric Code Topological Order from Rydberg Blockade","volume":"11","author":"Verresen","year":"2021","journal-title":"Phys. Rev. X"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"136","DOI":"10.21468\/SciPostPhys.14.5.136","article-title":"Systematic analysis of crystalline phases in bosonic lattice models with algebraically decaying density\u2013density interactions","volume":"14","author":"Koziol","year":"2023","journal-title":"SciPost Phys."},{"key":"ref_111","unstructured":"Koziol, J.A., Morigi, G., and Schmidt, K.P. (2023). Quantum phases of hard-core bosons with repulsive dipolar density\u2013density interactions on two-dimensional lattices. arXiv."},{"key":"ref_112","unstructured":"Duft, A., Koziol, J.A., Adelhardt, P., M\u00fchlhauser, M., and Schmidt, K.P. (2023). Order-by-disorder in the antiferromagnetic long-range transverse-field Ising model on the ruby lattice. arXiv."},{"key":"ref_113","doi-asserted-by":"crossref","unstructured":"Sachdev, S. (2011). Quantum Phase Transitions, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511973765"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s004070050021","article-title":"The Ehrenfest Classification of Phase Transitions: Introduction and Evolution","volume":"53","author":"Jaeger","year":"1998","journal-title":"Arch. Hist. Exact Sci."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1143\/PTP.56.1454","article-title":"Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations","volume":"56","author":"Suzuki","year":"1976","journal-title":"Prog. Theor. Phys."},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1103\/RevModPhys.69.315","article-title":"Continuous quantum phase transitions","volume":"69","author":"Sondhi","year":"1997","journal-title":"Rev. Mod. Phys."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"2069","DOI":"10.1088\/0034-4885\/66\/12\/R01","article-title":"Quantum phase transitions","volume":"66","author":"Vojta","year":"2003","journal-title":"Rep. Prog. Phys."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"3898","DOI":"10.1063\/1.1696618","article-title":"Equation of State in the Neighborhood of the Critical Point","volume":"43","author":"Widom","year":"1965","journal-title":"J. Chem. Phys."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1088\/0370-1328\/86\/5\/127","article-title":"On the critical behaviour of ferromagnets","volume":"86","author":"Domb","year":"1965","journal-title":"Proc. Phys. Soc."},{"key":"ref_120","first-page":"263","article-title":"Scaling laws for ising models near Tc","volume":"2","author":"Kadanoff","year":"1966","journal-title":"Phys. Phys. Fiz."},{"key":"ref_121","first-page":"292","article-title":"Behavior of ordered systems near the transition point","volume":"23","author":"Patashinskii","year":"1966","journal-title":"Sov. Phys. JETP"},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1088\/0034-4885\/30\/2\/306","article-title":"The theory of equilibrium critical phenomena","volume":"30","author":"Fisher","year":"1967","journal-title":"Rep. Prog. Phys."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1103\/RevModPhys.39.395","article-title":"Static Phenomena Near Critical Points: Theory and Experiment","volume":"39","author":"Kadanoff","year":"1967","journal-title":"Rev. Mod. Phys."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.1103\/PhysRevB.6.3515","article-title":"Systematic Application of Generalized Homogeneous Functions to Static Scaling, Dynamic Scaling, and Universality","volume":"6","author":"Hankey","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.nuclphysb.2004.05.012","article-title":"Finite size scaling for O(N) Phi4-theory at the upper critical dimension","volume":"691","author":"Kenna","year":"2004","journal-title":"Nucl. Phys. B"},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1051\/jphys:0198200430101500","article-title":"An investigation of finite size scaling","volume":"43","year":"1982","journal-title":"J. Phys. Fr."},{"key":"ref_127","doi-asserted-by":"crossref","unstructured":"Hahne, F.J.W. (1983). Critical Phenomena, Springer.","DOI":"10.1007\/3-540-12675-9"},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1103\/PhysRevB.31.1498","article-title":"Finite-size tests of hyperscaling","volume":"31","author":"Binder","year":"1985","journal-title":"Phys. Rev. B"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"214407","DOI":"10.1103\/PhysRevB.91.214407","article-title":"Exponent relations at quantum phase transitions with applications to metallic quantum ferromagnets","volume":"91","author":"Kirkpatrick","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1103\/PhysRevLett.17.1133","article-title":"Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models","volume":"17","author":"Mermin","year":"1966","journal-title":"Phys. Rev. Lett."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1103\/PhysRev.158.383","article-title":"Existence of Long-Range Order in One and Two Dimensions","volume":"158","author":"Hohenberg","year":"1967","journal-title":"Phys. Rev."},{"key":"ref_132","doi-asserted-by":"crossref","unstructured":"Kleinert, H., and Schulte-Frohlinde, V. (2001). Critical Properties of Phi4-Theories, World Scientific.","DOI":"10.1142\/9789812799944"},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"094404","DOI":"10.1103\/PhysRevB.91.094404","article-title":"Nonlinear bond-operator theory and 1\/d expansion for coupled-dimer magnets. I. Paramagnetic phase","volume":"91","author":"Joshi","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_134","doi-asserted-by":"crossref","first-page":"094405","DOI":"10.1103\/PhysRevB.91.094405","article-title":"Nonlinear bond-operator theory and 1\/d expansion for coupled-dimer magnets. II. Antiferromagnetic phase and quantum phase transition","volume":"91","author":"Joshi","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"125109","DOI":"10.1103\/PhysRevB.94.125109","article-title":"Linked-cluster expansions for quantum magnets on the hypercubic lattice","volume":"94","author":"Coester","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"3892","DOI":"10.1063\/1.1696617","article-title":"Surface Tension and Molecular Correlations near the Critical Point","volume":"43","author":"Widom","year":"1965","journal-title":"J. Chem. Phys."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1063\/1.1733766","article-title":"Pad\u00e9 Approximant Studies of the Lattice Gas and Ising Ferromagnet below the Critical Point","volume":"38","author":"Essam","year":"1963","journal-title":"J. Chem. Phys."},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1063\/1.1704197","article-title":"Correlation Functions and the Critical Region of Simple Fluids","volume":"5","author":"Fisher","year":"1964","journal-title":"J. Math. Phys."},{"key":"ref_139","unstructured":"Cardy, J. (1988). Finite-Size Scaling, Elsevier."},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1103\/RevModPhys.46.597","article-title":"The renormalization group in the theory of critical behavior","volume":"46","author":"Fisher","year":"1974","journal-title":"Rev. Mod. Phys."},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/S0370-1573(02)00219-3","article-title":"Critical phenomena and renormalization-group theory","volume":"368","author":"Pelissetto","year":"2002","journal-title":"Phys. Rep."},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01308937","article-title":"Critical properties and finite-size effects of the five-dimensional Ising model","volume":"61","author":"Binder","year":"1985","journal-title":"Z. Phys. B-Condens. Matter"},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1080\/00150198708227908","article-title":"Finite size effects on phase transitions","volume":"73","author":"Binder","year":"1987","journal-title":"Ferroelectrics"},{"key":"ref_144","doi-asserted-by":"crossref","unstructured":"Binder, K., and Heermann, D. (2019). Monte Carlo Simulation in Statistical Physics, Springer. Chapter 2.3.4.","DOI":"10.1007\/978-3-030-10758-1"},{"key":"ref_145","doi-asserted-by":"crossref","unstructured":"Cardy, J. (1996). Scaling and Renormalization in Statistical Physics, Cambridge University Press. Chapter 5.4.","DOI":"10.1017\/CBO9781316036440"},{"key":"ref_146","doi-asserted-by":"crossref","first-page":"3569","DOI":"10.1016\/S1573-4412(01)05010-3","article-title":"Chapter 57\u2014Markov Chain Monte Carlo Methods: Computation and Inference","volume":"Volume 5","author":"Chib","year":"2001","journal-title":"Handbook of Econometrics"},{"key":"ref_147","unstructured":"Levin, D.A., Peres, Y., and Wilmer, E.L. (2006). Markov Chains and Mixing Times, American Mathematical Society."},{"key":"ref_148","doi-asserted-by":"crossref","unstructured":"Krauth, W. (2006). Statistical Mechanics: Algorithms and Computations, Oxford University Press.","DOI":"10.1093\/oso\/9780198515357.001.0001"},{"key":"ref_149","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of State Calculations by Fast Computing Machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"ref_150","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","article-title":"Monte Carlo sampling methods using Markov chains and their applications","volume":"57","author":"Hastings","year":"1970","journal-title":"Biometrika"},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"663457","DOI":"10.3389\/fphy.2021.663457","article-title":"Event-Chain Monte Carlo: Foundations, Applications, and Prospects","volume":"9","author":"Krauth","year":"2021","journal-title":"Front. Phys."},{"key":"ref_152","doi-asserted-by":"crossref","first-page":"022118","DOI":"10.1103\/PhysRevE.92.022118","article-title":"Optimizing linked-cluster expansions by white graphs","volume":"92","author":"Coester","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_153","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s100510050026","article-title":"Perturbation theory by flow equations: Dimerized and frustrated S = 1\/2 chain","volume":"13","author":"Knetter","year":"2000","journal-title":"Eur. Phys. J. B"},{"key":"ref_154","doi-asserted-by":"crossref","first-page":"7889","DOI":"10.1088\/0305-4470\/36\/29\/302","article-title":"The structure of operators in effective particle-conserving models","volume":"36","author":"Knetter","year":"2003","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_155","doi-asserted-by":"crossref","unstructured":"Oitmaa, J., Hamer, C., and Zheng, W. (2006). Series Expansion Methods for Strongly Interacting Lattice Models, Cambridge University Press.","DOI":"10.1017\/CBO9780511584398"},{"key":"ref_156","doi-asserted-by":"crossref","first-page":"3958","DOI":"10.1103\/PhysRevLett.85.3958","article-title":"Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model","volume":"85","author":"Knetter","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"250402","DOI":"10.1103\/PhysRevLett.101.250402","article-title":"Theory of Magnetization Plateaux in the Shastry-Sutherland Model","volume":"101","author":"Dorier","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_158","doi-asserted-by":"crossref","first-page":"033109","DOI":"10.1103\/PhysRevB.79.033109","article-title":"Low-energy effective theory of the toric code model in a parallel magnetic field","volume":"79","author":"Vidal","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_159","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1088\/0305-4470\/14\/6\/009","article-title":"Quantum mechanical ground states, nonlinear Schrodinger equations and linked cluster expansions","volume":"14","author":"Kadanoff","year":"1981","journal-title":"J. Phys. Math. Gen."},{"key":"ref_160","doi-asserted-by":"crossref","first-page":"2047","DOI":"10.1088\/0305-4470\/14\/8\/027","article-title":"Series expansions for the zero-temperature transverse Ising model","volume":"14","author":"Marland","year":"1981","journal-title":"J. Phys. Math. Gen."},{"key":"ref_161","doi-asserted-by":"crossref","first-page":"2484","DOI":"10.1103\/PhysRevLett.61.2484","article-title":"Ground States of Low-Dimensional Quantum Antiferromagnets","volume":"61","author":"Singh","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_162","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0038-1098(96)00051-8","article-title":"Series expansions for excited states of quantum lattice models","volume":"98","author":"Gelfand","year":"1996","journal-title":"Solid State Commun."},{"key":"ref_163","doi-asserted-by":"crossref","first-page":"R15695","DOI":"10.1103\/PhysRevB.52.R15695","article-title":"Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets","volume":"52","author":"Singh","year":"1995","journal-title":"Phys. Rev. B"},{"key":"ref_164","doi-asserted-by":"crossref","first-page":"4373","DOI":"10.1103\/PhysRevLett.85.4373","article-title":"Strong-Coupling Expansions for Multiparticle Excitations: Continuum and Bound States","volume":"85","author":"Trebst","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_165","doi-asserted-by":"crossref","first-page":"144410","DOI":"10.1103\/PhysRevB.63.144410","article-title":"Linked cluster series expansions for two-particle bound states","volume":"63","author":"Zheng","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_166","doi-asserted-by":"crossref","first-page":"267204","DOI":"10.1103\/PhysRevLett.105.267204","article-title":"Effective Spin Model for the Spin-Liquid Phase of the Hubbard Model on the Triangular Lattice","volume":"105","author":"Yang","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_167","doi-asserted-by":"crossref","first-page":"064412","DOI":"10.1103\/PhysRevB.81.064412","article-title":"Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study","volume":"81","author":"Dusuel","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_168","doi-asserted-by":"crossref","first-page":"054404","DOI":"10.1103\/PhysRevB.87.054404","article-title":"Disorder by disorder and flat bands in the kagome transverse field Ising model","volume":"87","author":"Powalski","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_169","doi-asserted-by":"crossref","first-page":"147203","DOI":"10.1103\/PhysRevLett.110.147203","article-title":"Topological Phase Transitions in the Golden String-Net Model","volume":"110","author":"Schulz","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_170","doi-asserted-by":"crossref","first-page":"201103","DOI":"10.1103\/PhysRevB.89.201103","article-title":"Ising anyons with a string tension","volume":"89","author":"Schulz","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_171","doi-asserted-by":"crossref","first-page":"097","DOI":"10.21468\/SciPostPhys.15.3.097","article-title":"Projective cluster-additive transformation for quantum lattice models","volume":"15","author":"Schmidt","year":"2023","journal-title":"SciPost Phys."},{"key":"ref_172","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1007\/BF01899329","article-title":"Ein infinitesimales Analogon zum Quotienten-Differenzen-Algorithmus","volume":"5","author":"Rutishauser","year":"1954","journal-title":"Arch. Math."},{"key":"ref_173","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1143\/JPSJ.22.431","article-title":"Vibration of a Chain with Nonlinear Interaction","volume":"22","author":"Toda","year":"1967","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_174","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1103\/PhysRevB.9.1924","article-title":"The Toda lattice. II. Existence of integrals","volume":"9","author":"Flaschka","year":"1974","journal-title":"Phys. Rev. B"},{"key":"ref_175","doi-asserted-by":"crossref","unstructured":"Moser, J. (1975). Dynamical Systems, Theory and Applications: Battelle Seattle 1974 Rencontres, Springer.","DOI":"10.1007\/3-540-07171-7"},{"key":"ref_176","unstructured":"Brockett, R. (1988, January 7\u20139). Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems. Proceedings of the 27th IEEE Conference on Decision and Control, Austin, TX, USA."},{"key":"ref_177","doi-asserted-by":"crossref","first-page":"5863","DOI":"10.1103\/PhysRevD.48.5863","article-title":"Renormalization of Hamiltonians","volume":"48","author":"Wilson","year":"1993","journal-title":"Phys. Rev. D"},{"key":"ref_178","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1002\/andp.19945060203","article-title":"Flow-equations for Hamiltonians","volume":"506","author":"Wegner","year":"1994","journal-title":"Ann. Phys."},{"key":"ref_179","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/BF02508481","article-title":"Flow equations and the strong-coupling expansion for the Hubbard model","volume":"88","author":"Stein","year":"1997","journal-title":"J. Stat. Phys."},{"key":"ref_180","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s100510050485","article-title":"Flow equations for band-matrices","volume":"5","author":"Mielke","year":"1998","journal-title":"Eur. Phys. J. B"},{"key":"ref_181","unstructured":"Schulz, M.D. (2013). Topological Phase Transitions Driven by Non-Abelian Anyons. [Ph.D. Thesis, Universit\u00e9 Pierre-et-Marie-Curie]."},{"key":"ref_182","doi-asserted-by":"crossref","unstructured":"Coester, K. (2015). Quasiparticle Pictures and Graphs\u2014From Perturbative to Non-Perturbative Linked-Cluster Expansions. [Ph.D. Thesis, TU Dortmund].","DOI":"10.1209\/0295-5075\/110\/20006"},{"key":"ref_183","doi-asserted-by":"crossref","first-page":"12267","DOI":"10.1103\/PhysRevB.55.12267","article-title":"Various series expansions for the bilayer S = 12 Heisenberg antiferromagnet","volume":"55","author":"Weihong","year":"1997","journal-title":"Phys. Rev. B"},{"key":"ref_184","doi-asserted-by":"crossref","first-page":"054419","DOI":"10.1103\/PhysRevB.78.054419","article-title":"Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system","volume":"78","author":"Collins","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_185","doi-asserted-by":"crossref","first-page":"230508","DOI":"10.1103\/PhysRevLett.108.230508","article-title":"Constraints on Measurement-Based Quantum Computation in Effective Cluster States","volume":"108","author":"Klagges","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_186","doi-asserted-by":"crossref","first-page":"023098","DOI":"10.1103\/PhysRevResearch.2.023098","article-title":"Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice","volume":"2","author":"Boos","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"ref_187","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/000187300243390","article-title":"High-order convergent expansions for quantum many particle systems","volume":"49","author":"Gelfand","year":"2000","journal-title":"Adv. Phys."},{"key":"ref_188","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1063\/1.3667323","article-title":"The Density Matrix Renormalization Group and its time-dependent variants","volume":"1419","author":"Feiguin","year":"2011","journal-title":"AIP Conf. Proc."},{"key":"ref_189","doi-asserted-by":"crossref","unstructured":"Squires, G.L. (2012). Introduction to the Theory of Thermal Neutron Scattering, Cambridge University Press. [3rd ed.].","DOI":"10.1017\/CBO9781139107808"},{"key":"ref_190","doi-asserted-by":"crossref","unstructured":"Avella, A., and Mancini, F. (2015). Strongly Correlated Systems: Experimental Techniques, Springer.","DOI":"10.1007\/978-3-662-44133-6"},{"key":"ref_191","doi-asserted-by":"crossref","first-page":"214408","DOI":"10.1103\/PhysRevB.68.214408","article-title":"Dynamical structure factor for the alternating Heisenberg chain: A linked cluster calculation","volume":"68","author":"Hamer","year":"2003","journal-title":"Phys. Rev. B"},{"key":"ref_192","doi-asserted-by":"crossref","first-page":"124205","DOI":"10.1088\/0953-8984\/21\/12\/124205","article-title":"Critical behaviour of structure factors at a quantum phase transition","volume":"21","author":"Hamer","year":"2009","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_193","doi-asserted-by":"crossref","unstructured":"Rahman, M.S. (2017). Basic Graph Theory, Springer.","DOI":"10.1007\/978-3-319-49475-3"},{"key":"ref_194","doi-asserted-by":"crossref","unstructured":"Harary, F. (1969). Graph Theory, Addison-Wesley Publishing Company.","DOI":"10.21236\/AD0705364"},{"key":"ref_195","unstructured":"M\u00fchlhauser, M. (2024). Graph Decomposition Techniques and Their Application to Topological Systems. [Ph.D. Thesis, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg]. To be published."},{"key":"ref_196","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1145\/3372123","article-title":"The graph isomorphism problem","volume":"63","author":"Grohe","year":"2020","journal-title":"Commun. ACM"},{"key":"ref_197","doi-asserted-by":"crossref","unstructured":"Bonnici, V., Giugno, R., Pulvirenti, A., Shasha, D., and Ferro, A. (2013). A subgraph isomorphism algorithm and its application to biochemical data. BMC Bioinform., 14.","DOI":"10.1186\/1471-2105-14-S7-S13"},{"key":"ref_198","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1109\/TCBB.2016.2515595","article-title":"On the Variable Ordering in Subgraph Isomorphism Algorithms","volume":"14","author":"Bonnici","year":"2017","journal-title":"IEEE\/ACM Trans. Comput. Biol. Bioinform."},{"key":"ref_199","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1090\/conm\/479\/09345","article-title":"Mckay\u2019s canonical graph labeling algorithm","volume":"479","author":"Hartke","year":"2009","journal-title":"Commun. Math."},{"key":"ref_200","first-page":"45","article-title":"Practical graph isomorphism","volume":"30","author":"McKay","year":"1981","journal-title":"Congr. Numer."},{"key":"ref_201","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.jsc.2013.09.003","article-title":"Practical graph isomorphism, II","volume":"60","author":"McKay","year":"2014","journal-title":"J. Symb. Comput."},{"key":"ref_202","unstructured":"Varoquaux, G., Vaught, T., and Millman, J. (2008, January 19\u201324). Exploring Network Structure, Dynamics, and Function using NetworkX. Proceedings of the 7th Python in Science Conference, Pasadena, CA, USA."},{"key":"ref_203","unstructured":"Siek, J., Lee, L., and Lumsdaine, A. (2001). The Boost Graph Library: User Guide and Reference Manual, Pearson Education."},{"key":"ref_204","unstructured":"Jahromi, S.S., H\u00f6rmann, M., Adelhardt, P., Fey, S., Orus, R., and Schmidt, K.P. (2021). Kitaev honeycomb antiferromagnet in a field: Quantum phase diagram for general spin. arXiv."},{"key":"ref_205","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.aop.2005.10.005","article-title":"Anyons in an exactly solved model and beyond","volume":"321","author":"Kitaev","year":"2006","journal-title":"Ann. Phys."},{"key":"ref_206","unstructured":"Adelhardt, P., and Schmidt, K.P. (2024). Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Bavaria, Germany, in press."},{"key":"ref_207","unstructured":"Fey, S. (2020). Investigation of Zero-Temperature Transverse-Field Ising Models with Long-Range Interactions. [Ph.D. Thesis, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg]."},{"key":"ref_208","unstructured":"Baker, G. (1975). Essentials of Pad\u00e9 Approximants, Elsevier Science."},{"key":"ref_209","unstructured":"Domb, C., Green, M.S., and Lebowitz, J.L. (1989). Phase Transitions and Critical Phenomena, Academic Press."},{"key":"ref_210","doi-asserted-by":"crossref","first-page":"5950","DOI":"10.1103\/PhysRevB.43.5950","article-title":"Quantum Monte Carlo simulation method for spin systems","volume":"43","author":"Sandvik","year":"1991","journal-title":"Phys. Rev. B"},{"key":"ref_211","doi-asserted-by":"crossref","first-page":"14510","DOI":"10.1103\/PhysRevB.56.14510","article-title":"Quantum Monte Carlo in the interaction representation: Application to a spin-Peierls model","volume":"56","author":"Sandvik","year":"1997","journal-title":"Phys. Rev. B"},{"key":"ref_212","unstructured":"Humeniuk, S. (2018). Quantum Monte Carlo Studies of Strongly Correlated Systems for Quantum Simulators. [Ph.D. Thesis, Fakult\u00e4t Mathematik und Physik, Universit\u00e4t Stuttgart]."},{"key":"ref_213","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1063\/1.3518900","article-title":"Computational Studies of Quantum Spin Systems","volume":"1297","author":"Sandvik","year":"2010","journal-title":"AIP Conf. Proc."},{"key":"ref_214","doi-asserted-by":"crossref","first-page":"2629","DOI":"10.1016\/j.jcp.2008.12.022","article-title":"Order-N cluster Monte Carlo method for spin systems with long-range interactions","volume":"228","author":"Fukui","year":"2009","journal-title":"J. Comput. Phys."},{"key":"ref_215","doi-asserted-by":"crossref","first-page":"046701","DOI":"10.1103\/PhysRevE.66.046701","article-title":"Quantum Monte Carlo with directed loops","volume":"66","author":"Sandvik","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_216","doi-asserted-by":"crossref","first-page":"R14157","DOI":"10.1103\/PhysRevB.59.R14157","article-title":"Stochastic series expansion method with operator-loop update","volume":"59","author":"Sandvik","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_217","doi-asserted-by":"crossref","first-page":"036706","DOI":"10.1103\/PhysRevE.71.036706","article-title":"Generalized directed loop method for quantum Monte Carlo simulations","volume":"71","author":"Alet","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_218","doi-asserted-by":"crossref","first-page":"3667","DOI":"10.1088\/0305-4470\/25\/13\/017","article-title":"A generalization of Handscomb\u2019s quantum Monte Carlo scheme-application to the 1D Hubbard model","volume":"25","author":"Sandvik","year":"1992","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_219","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1143\/JPSJ.12.570","article-title":"Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems","volume":"12","author":"Kubo","year":"1957","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_220","unstructured":"Michel, F., and Evertz, H.G. (2007). Lattice dynamics of the Heisenberg chain coupled to finite frequency bond phonons. arXiv."},{"key":"ref_221","first-page":"594","article-title":"Finite-size correlation length and violations of finite-size scaling","volume":"20","author":"Caracciolo","year":"2001","journal-title":"Eur. Phys. J. B"},{"key":"ref_222","unstructured":"Sadhukhan, D., and Dziarmaga, J. (2021). Is there a correlation length in a model with long-range interactions?. arXiv."},{"key":"ref_223","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/0378-4371(92)90063-V","article-title":"Finite-size scaling for systems with long-range interactions","volume":"189","author":"Brankov","year":"1992","journal-title":"Phys. A"},{"key":"ref_224","doi-asserted-by":"crossref","unstructured":"Flores-Sola, E.J. (2016). Finite-Size Scaling above the Upper Critical Dimension. [Ph.D. Thesis, Universit\u00e9 de Lorraine, Nancy, France; Coventry University].","DOI":"10.1103\/PhysRevLett.116.115701"},{"key":"ref_225","doi-asserted-by":"crossref","first-page":"024418","DOI":"10.1103\/PhysRevB.66.024418","article-title":"Classical percolation transition in the diluted two-dimensional S = 12 Heisenberg antiferromagnet","volume":"66","author":"Sandvik","year":"2002","journal-title":"Phys. Rev. B"},{"key":"ref_226","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0375-9601(97)00957-2","article-title":"\u201cWorm\u201d algorithm in quantum Monte Carlo simulations","volume":"238","author":"Svistunov","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_227","doi-asserted-by":"crossref","first-page":"2249","DOI":"10.1016\/j.jcp.2007.03.013","article-title":"Engineering local optimality in quantum Monte Carlo algorithms","volume":"225","author":"Pollet","year":"2007","journal-title":"J. Comput. Phys."},{"key":"ref_228","doi-asserted-by":"crossref","first-page":"073036","DOI":"10.1088\/1367-2630\/11\/7\/073036","article-title":"Sign-alternating interaction mediated by strongly correlated lattice bosons","volume":"11","author":"Svistunov","year":"2009","journal-title":"New J. Phys."},{"key":"ref_229","doi-asserted-by":"crossref","first-page":"125302","DOI":"10.1103\/PhysRevLett.104.125302","article-title":"Supersolid Phase with Cold Polar Molecules on a Triangular Lattice","volume":"104","author":"Pollet","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_230","doi-asserted-by":"crossref","first-page":"113006","DOI":"10.1088\/1367-2630\/14\/11\/113006","article-title":"Quantum spin models with long-range interactions and tunnelings: A quantum Monte Carlo study","volume":"14","author":"Maik","year":"2012","journal-title":"New J. Phys."},{"key":"ref_231","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1103\/PhysRevB.40.546","article-title":"Boson localization and the superfluid-insulator transition","volume":"40","author":"Fisher","year":"1989","journal-title":"Phys. Rev. B"},{"key":"ref_232","doi-asserted-by":"crossref","first-page":"3144","DOI":"10.1103\/PhysRevLett.66.3144","article-title":"Localization in interacting, disordered, Bose systems","volume":"66","author":"Scalettar","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_233","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1103\/PhysRevLett.67.2307","article-title":"Superfluid-insulator transition in disordered boson systems","volume":"67","author":"Krauth","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_234","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.1103\/PhysRevLett.84.1599","article-title":"Phase Separation in Supersolids","volume":"84","author":"Batrouni","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_235","doi-asserted-by":"crossref","first-page":"014513","DOI":"10.1103\/PhysRevB.65.014513","article-title":"Quantum phase transitions in the two-dimensional hard-core boson model","volume":"65","author":"Batrouni","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_236","doi-asserted-by":"crossref","first-page":"245102","DOI":"10.1103\/PhysRevB.97.245102","article-title":"Extended Bose\u2013Hubbard model with dipolar and contact interactions","volume":"97","author":"Zakrzewski","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_237","doi-asserted-by":"crossref","first-page":"174505","DOI":"10.1103\/PhysRevB.101.174505","article-title":"Superfluid phases induced by dipolar interactions","volume":"101","author":"Kraus","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_238","doi-asserted-by":"crossref","first-page":"035144","DOI":"10.1103\/PhysRevB.106.035144","article-title":"Quantum phases of dipolar bosons in one-dimensional optical lattices","volume":"106","author":"Kraus","year":"2022","journal-title":"Phys. Rev. B"},{"key":"ref_239","doi-asserted-by":"crossref","first-page":"5033","DOI":"10.1103\/PhysRevB.26.5033","article-title":"Monte Carlo simulations of one-dimensional fermion systems","volume":"26","author":"Hirsch","year":"1982","journal-title":"Phys. Rev. B"},{"key":"ref_240","doi-asserted-by":"crossref","first-page":"5130","DOI":"10.1103\/PhysRevLett.77.5130","article-title":"Simulations of Discrete Quantum Systems in Continuous Euclidean Time","volume":"77","author":"Beard","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_241","unstructured":"Landau, D.P., Lewis, S.P., and Sch\u00fcttler, H.B. (2001, January 19\u201324). The Stochastic Series Expansion Method for Quantum Lattice Models. Proceedings of the Computer Simulation Studies in Condensed-Matter Physics XIV, Athens, GA, USA."},{"key":"ref_242","doi-asserted-by":"crossref","unstructured":"Fehske, H., Schneider, R., and Wei\u00dfe, A. (2008). Computational Many-Particle Physics, Springer.","DOI":"10.1007\/978-3-540-74686-7"},{"key":"ref_243","doi-asserted-by":"crossref","first-page":"073201","DOI":"10.1103\/PhysRevLett.118.073201","article-title":"Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice","volume":"118","author":"Schindewolf","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_244","doi-asserted-by":"crossref","first-page":"143001","DOI":"10.1088\/1751-8121\/ab6a6c","article-title":"Criticality of spin systems with weak long-range interactions","volume":"53","author":"Defenu","year":"2020","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_245","doi-asserted-by":"crossref","first-page":"214302","DOI":"10.1103\/PhysRevB.85.214302","article-title":"Quantum criticality in spin chains with non-Ohmic dissipation","volume":"85","author":"Sperstad","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_246","doi-asserted-by":"crossref","first-page":"2370","DOI":"10.1088\/0022-3719\/4\/15\/024","article-title":"The Ising model with a transverse field. II. Ground state properties","volume":"4","author":"Pfeuty","year":"1971","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_247","doi-asserted-by":"crossref","unstructured":"Langheld, A., Koziol, J.A., Adelhardt, P., Kapfer, S.C., and Schmidt, K.P. (2021). Raw data to \u201cScaling at quantum phase transitions above the upper critical dimension\u201d. Zenodo.","DOI":"10.21468\/SciPostPhys.13.4.088-update-1"},{"key":"ref_248","doi-asserted-by":"crossref","first-page":"032115","DOI":"10.1103\/PhysRevA.100.032115","article-title":"Quantum Kibble-Zurek physics in long-range transverse-field Ising models","volume":"100","author":"Puebla","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_249","doi-asserted-by":"crossref","unstructured":"Koziol, J.A., Langheld, A., Kapfer, S.C., and Schmidt, K.P. (2021). Raw data to \u201cQuantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations\u201d. Zenodo.","DOI":"10.1103\/PhysRevB.103.245135"},{"key":"ref_250","unstructured":"Shiratani, S., and Todo, S. (2023). Stochastic approximation analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain. arXiv."},{"key":"ref_251","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1103\/PhysRevLett.25.443","article-title":"Ising Model with a Transverse Field","volume":"25","author":"Elliott","year":"1970","journal-title":"Phys. Rev. Lett."},{"key":"ref_252","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0003-4916(70)90270-8","article-title":"The one-dimensional Ising model with a transverse field","volume":"57","author":"Pfeuty","year":"1970","journal-title":"Ann. Phys."},{"key":"ref_253","doi-asserted-by":"crossref","unstructured":"Kos, F., Poland, D., Simmons-Duffin, D., and Vichi, A. (2016). Precision islands in the Ising and O(N) models. J. High Energy Phys., 2016.","DOI":"10.1007\/JHEP08(2016)036"},{"key":"ref_254","doi-asserted-by":"crossref","first-page":"021106","DOI":"10.1103\/PhysRevE.78.021106","article-title":"Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections","volume":"78","author":"Ribeiro","year":"2008","journal-title":"Phys. Rev. E"},{"key":"ref_255","doi-asserted-by":"crossref","first-page":"220601","DOI":"10.1103\/PhysRevLett.96.220601","article-title":"Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States","volume":"96","author":"Verstraete","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_256","doi-asserted-by":"crossref","first-page":"045003","DOI":"10.1103\/RevModPhys.93.045003","article-title":"Matrix product states and projected entangled pair states: Concepts, symmetries, theorems","volume":"93","author":"Cirac","year":"2021","journal-title":"Rev. Mod. Phys."},{"key":"ref_257","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1146\/annurev-conmatphys-020911-125018","article-title":"Studying Two-Dimensional Systems with the Density Matrix Renormalization Group","volume":"3","author":"Stoudenmire","year":"2012","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_258","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1103\/RevModPhys.82.277","article-title":"Colloquium: Area laws for the entanglement entropy","volume":"82","author":"Eisert","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"ref_259","doi-asserted-by":"crossref","first-page":"035116","DOI":"10.1103\/PhysRevB.78.035116","article-title":"Applying matrix product operators to model systems with long-range interactions","volume":"78","author":"Crosswhite","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_260","doi-asserted-by":"crossref","first-page":"025012","DOI":"10.1088\/1367-2630\/12\/2\/025012","article-title":"Matrix product operator representations","volume":"12","author":"Pirvu","year":"2010","journal-title":"New J. Phys."},{"key":"ref_261","doi-asserted-by":"crossref","first-page":"235103","DOI":"10.1103\/PhysRevB.93.235103","article-title":"Quantum cluster algorithm for frustrated Ising models in a transverse field","volume":"93","author":"Biswas","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_262","doi-asserted-by":"crossref","first-page":"085114","DOI":"10.1103\/PhysRevB.97.085114","article-title":"Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice","volume":"97","author":"Biswas","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_263","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1103\/PhysRev.65.117","article-title":"Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition","volume":"65","author":"Onsager","year":"1944","journal-title":"Phys. Rev."},{"key":"ref_264","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1063\/1.2186278","article-title":"Geometrical frustration","volume":"59","author":"Moessner","year":"2006","journal-title":"Phys. Today"},{"key":"ref_265","doi-asserted-by":"crossref","first-page":"12049","DOI":"10.1103\/PhysRevB.58.12049","article-title":"Low-temperature properties of classical geometrically frustrated antiferromagnets","volume":"58","author":"Moessner","year":"1998","journal-title":"Phys. Rev. B"},{"key":"ref_266","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1080\/14786446408643668","article-title":"L. on the calculation of the equilibrium and stiffness of frames","volume":"27","author":"Maxwell","year":"1864","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"ref_267","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1103\/PhysRevB.43.865","article-title":"Mean-field approach to magnetic ordering in highly frustrated pyrochlores","volume":"43","author":"Reimers","year":"1991","journal-title":"Phys. Rev. B"},{"key":"ref_268","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1103\/PhysRev.79.357","article-title":"Antiferromagnetism. The Triangular Ising Net","volume":"79","author":"Wannier","year":"1950","journal-title":"Phys. Rev."},{"key":"ref_269","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1143\/ptp\/10.2.158","article-title":"Antiferromagnetism. The Kagome Ising Net","volume":"10","author":"Kano","year":"1953","journal-title":"Prog. Theor. Phys."},{"key":"ref_270","doi-asserted-by":"crossref","first-page":"4457","DOI":"10.1103\/PhysRevLett.84.4457","article-title":"Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field","volume":"84","author":"Moessner","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_271","doi-asserted-by":"crossref","first-page":"224401","DOI":"10.1103\/PhysRevB.63.224401","article-title":"Ising models of quantum frustration","volume":"63","author":"Moessner","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_272","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1051\/jphys:0198000410110126300","article-title":"Order as an effect of disorder","volume":"41","author":"Villain","year":"1980","journal-title":"J. Phys."},{"key":"ref_273","doi-asserted-by":"crossref","first-page":"104409","DOI":"10.1103\/PhysRevB.68.104409","article-title":"Interplay of quantum and thermal fluctuations in a frustrated magnet","volume":"68","author":"Isakov","year":"2003","journal-title":"Phys. Rev. B"},{"key":"ref_274","doi-asserted-by":"crossref","first-page":"134424","DOI":"10.1103\/PhysRevB.64.134424","article-title":"Disorder from disorder in a strongly frustrated transverse-field Ising chain","volume":"64","author":"Priour","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_275","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1038\/nature08917","article-title":"Spin liquids in frustrated magnets","volume":"464","author":"Balents","year":"2010","journal-title":"Nature"},{"key":"ref_276","doi-asserted-by":"crossref","first-page":"201111","DOI":"10.1103\/PhysRevB.94.201111","article-title":"Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model","volume":"94","author":"Balents","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_277","doi-asserted-by":"crossref","unstructured":"Koziol, J.A., M\u00fchlhauser, M., and Schmidt, K.P. (2024). Order-by-disorder and long-range interactions in the antiferromagnetic transverse-field Ising model on the triangular lattice\u2014A perturbative point of view. arXiv.","DOI":"10.1016\/j.rinp.2024.107794"},{"key":"ref_278","doi-asserted-by":"crossref","first-page":"2376","DOI":"10.1103\/PhysRevLett.61.2376","article-title":"Superconductivity and the Quantum Hard-Core Dimer Gas","volume":"61","author":"Rokhsar","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_279","doi-asserted-by":"crossref","first-page":"197201","DOI":"10.1103\/PhysRevLett.116.197201","article-title":"Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets","volume":"116","author":"Smerald","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_280","doi-asserted-by":"crossref","first-page":"030","DOI":"10.21468\/SciPostPhys.5.3.030","article-title":"Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet","volume":"5","author":"Smerald","year":"2018","journal-title":"SciPost Phys."},{"key":"ref_281","doi-asserted-by":"crossref","first-page":"224517","DOI":"10.1103\/PhysRevB.100.224517","article-title":"Monte Carlo study of an improved clock model in three dimensions","volume":"100","author":"Hasenbusch","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_282","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/JHEP06(2020)142","article-title":"Carving out OPE space and precise O(2) model critical exponents","volume":"2020","author":"Chester","year":"2020","journal-title":"J. High Energy Phys."},{"key":"ref_283","doi-asserted-by":"crossref","first-page":"206501","DOI":"10.1103\/PhysRevLett.130.206501","article-title":"Emergent Glassy Behavior in a Kagome Rydberg Atom Array","volume":"130","author":"Yan","year":"2023","journal-title":"Phys. Rev. Lett."},{"key":"ref_284","doi-asserted-by":"crossref","first-page":"4412","DOI":"10.1103\/PhysRevLett.76.4412","article-title":"Multicritical Crossovers near the Dilute Bose Gas Quantum Critical Point","volume":"76","author":"Damle","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_285","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0003-4916(61)90115-4","article-title":"Two soluble models of an antiferromagnetic chain","volume":"16","author":"Lieb","year":"1961","journal-title":"Ann. Phys."},{"key":"ref_286","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1103\/PhysRev.173.531","article-title":"Spin Correlation Functions of the X-Y Model","volume":"173","author":"McCoy","year":"1968","journal-title":"Phys. Rev."},{"key":"ref_287","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1103\/PhysRevA.2.1075","article-title":"Statistical Mechanics of the XY Model. I","volume":"2","author":"Barouch","year":"1970","journal-title":"Phys. Rev. A"},{"key":"ref_288","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1103\/PhysRevA.3.786","article-title":"Statistical Mechanics of the XY Model. II. Spin-Correlation Functions","volume":"3","author":"Barouch","year":"1971","journal-title":"Phys. Rev. A"},{"key":"ref_289","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.1103\/PhysRevA.3.2137","article-title":"Statistical Mechanics of the XY Model. III","volume":"3","author":"Barouch","year":"1971","journal-title":"Phys. Rev. A"},{"key":"ref_290","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1103\/PhysRevA.4.2331","article-title":"Statistical Mechanics of the XY Model. IV. Time-Dependent Spin-Correlation Functions","volume":"4","author":"McCoy","year":"1971","journal-title":"Phys. Rev. A"},{"key":"ref_291","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/0167-2789(80)90006-8","article-title":"Density matrix of an impenetrable Bose gas and the fifth Painlev\u00e9 transcendent","volume":"1","author":"Jimbo","year":"1980","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_292","doi-asserted-by":"crossref","first-page":"2741","DOI":"10.1088\/0305-4470\/14\/10\/026","article-title":"Finite size scaling and crossover phenomena: The XY chain in a transverse field at zero temperature","volume":"14","author":"Santos","year":"1981","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_293","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/0375-9601(83)90255-4","article-title":"Exact ground-state excitations of the XY model in a transverse field in one dimension","volume":"98","author":"Ray","year":"1983","journal-title":"Phys. Lett. A"},{"key":"ref_294","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0375-9601(81)90602-2","article-title":"On the zero temperature critical behaviour of the nonideal Bose gas","volume":"87","author":"Uzunov","year":"1981","journal-title":"Phys. Lett. A"},{"key":"ref_295","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF01646487","article-title":"There are no Goldstone bosons in two dimensions","volume":"31","author":"Coleman","year":"1973","journal-title":"Commun. Math. Phys."},{"key":"ref_296","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF00682193","article-title":"Uncertainty principle, quantum fluctuations, and broken symmetries","volume":"85","author":"Pitaevskii","year":"1991","journal-title":"J. Low Temp. Phys."},{"key":"ref_297","doi-asserted-by":"crossref","first-page":"137204","DOI":"10.1103\/PhysRevLett.104.137204","article-title":"Ground States of a Frustrated Quantum Spin Chain with Long-Range Interactions","volume":"104","author":"Sandvik","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_298","doi-asserted-by":"crossref","first-page":"134412","DOI":"10.1103\/PhysRevB.88.134412","article-title":"Decoupled phase of frustrated spin-12 antiferromagnetic chains with and without long-range order in the ground state","volume":"88","author":"Kumar","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_299","doi-asserted-by":"crossref","first-page":"235110","DOI":"10.1103\/PhysRevB.91.235110","article-title":"Matrix product state approach to a frustrated spin chain with long-range interactions","volume":"91","author":"Li","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_300","doi-asserted-by":"crossref","first-page":"184425","DOI":"10.1103\/PhysRevB.92.184425","article-title":"Quantum Monte Carlo studies of spinons in one-dimensional spin systems","volume":"92","author":"Tang","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_301","doi-asserted-by":"crossref","first-page":"205115","DOI":"10.1103\/PhysRevB.93.205115","article-title":"Kaleidoscope of quantum phases in a long-range interacting spin-1 chain","volume":"93","author":"Gong","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_302","doi-asserted-by":"crossref","first-page":"023001","DOI":"10.1103\/PhysRevLett.119.023001","article-title":"Continuous Symmetry Breaking in 1D Long-Range Interacting Quantum Systems","volume":"119","author":"Maghrebi","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_303","doi-asserted-by":"crossref","first-page":"245111","DOI":"10.1103\/PhysRevB.95.245111","article-title":"Entanglement and fluctuations in the XXZ model with power-law interactions","volume":"95","author":"Naldesi","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_304","doi-asserted-by":"crossref","first-page":"024425","DOI":"10.1103\/PhysRevB.102.024425","article-title":"Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy","volume":"102","author":"Ren","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_305","doi-asserted-by":"crossref","first-page":"110","DOI":"10.21468\/SciPostPhys.10.5.110","article-title":"From deconfined spinons to coherent magnons in an antiferromagnetic Heisenberg chain with long range interactions","volume":"10","author":"Yang","year":"2021","journal-title":"SciPost Phys."},{"key":"ref_306","doi-asserted-by":"crossref","first-page":"60","DOI":"10.21468\/SciPostPhys.13.3.060","article-title":"Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions","volume":"13","author":"Yang","year":"2022","journal-title":"SciPost Phys."},{"key":"ref_307","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1140\/epjb\/s10051-021-00245-1","article-title":"Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: Anisotropy-driven multi-criticality","volume":"94","author":"Nishiyama","year":"2021","journal-title":"Eur. Phys. J. B"},{"key":"ref_308","doi-asserted-by":"crossref","first-page":"2418","DOI":"10.1103\/PhysRevD.8.2418","article-title":"Approach to Scaling in Renormalized Perturbation Theory","volume":"8","author":"Brezin","year":"1973","journal-title":"Phys. Rev. D"},{"key":"ref_309","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1103\/PhysRevB.7.248","article-title":"Logarithmic Corrections to the Molecular-Field Behavior of Critical and Tricritical Systems","volume":"7","author":"Wegner","year":"1973","journal-title":"Phys. Rev. B"},{"key":"ref_310","doi-asserted-by":"crossref","first-page":"5425","DOI":"10.1088\/0305-4470\/27\/16\/010","article-title":"Series expansions for the 3D transverse Ising model at T=0","volume":"27","author":"Weihong","year":"1994","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_311","doi-asserted-by":"crossref","first-page":"127205","DOI":"10.1103\/PhysRevLett.95.127205","article-title":"Supersolid Hard-Core Bosons on the Triangular Lattice","volume":"95","author":"Wessel","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_312","doi-asserted-by":"crossref","first-page":"083102","DOI":"10.1088\/1742-5468\/aceb55","article-title":"Transverse-field XY spin chain with the competing long-range interactions: Multi-criticality around the XX-symmetric point","volume":"2023","author":"Nishiyama","year":"2023","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_313","doi-asserted-by":"crossref","first-page":"9323","DOI":"10.1103\/PhysRevB.41.9323","article-title":"Bond-operator representation of quantum spins: Mean-field theory of frustrated quantum Heisenberg antiferromagnets","volume":"41","author":"Sachdev","year":"1990","journal-title":"Phys. Rev. B"},{"key":"ref_314","doi-asserted-by":"crossref","first-page":"167201","DOI":"10.1103\/PhysRevLett.121.167201","article-title":"Dynamic Structure Factor of Disordered Quantum Spin Ladders","volume":"121","author":"Wunderlich","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_315","doi-asserted-by":"crossref","first-page":"227204","DOI":"10.1103\/PhysRevLett.90.227204","article-title":"Excitations in One-Dimensional S = 12 Quantum Antiferromagnets","volume":"90","author":"Schmidt","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_316","doi-asserted-by":"crossref","first-page":"137203","DOI":"10.1103\/PhysRevLett.87.137203","article-title":"Absence of Spontaneous Magnetic Order at Nonzero Temperature in One- and Two-Dimensional Heisenberg and XY Systems with Long-Range Interactions","volume":"87","author":"Bruno","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_317","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1088\/0305-4470\/30\/4\/012","article-title":"N\u00e9el order in the ground state of Heisenberg antiferromagnetic chains with long-range interactions","volume":"30","author":"Parreira","year":"1997","journal-title":"J.-Phys.-Lond.-Math. Gen."},{"key":"ref_318","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1103\/PhysRev.117.648","article-title":"Quasi-Particles and Gauge Invariance in the Theory of Superconductivity","volume":"117","author":"Nambu","year":"1960","journal-title":"Phys. Rev."},{"key":"ref_319","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/BF02812722","article-title":"Field theories with \u00ab Superconductor \u00bb solutions","volume":"19","author":"Goldstone","year":"1961","journal-title":"Il Nuovo C."},{"key":"ref_320","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1103\/PhysRev.127.965","article-title":"Broken Symmetries","volume":"127","author":"Goldstone","year":"1962","journal-title":"Phys. Rev."},{"key":"ref_321","doi-asserted-by":"crossref","first-page":"033038","DOI":"10.1103\/PhysRevResearch.5.033038","article-title":"Generalized Higgs mechanism in long-range-interacting quantum systems","volume":"5","author":"Diessel","year":"2023","journal-title":"Phys. Rev. Res."},{"key":"ref_322","doi-asserted-by":"crossref","first-page":"144412","DOI":"10.1103\/PhysRevB.69.144412","article-title":"Spin waves in antiferromagnetic spin chains with long-range interactions","volume":"69","author":"Yusuf","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_323","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1103\/PhysRev.146.301","article-title":"Nonrelativistic Theorem Analogous to the Goldstone Theorem","volume":"146","author":"Lange","year":"1966","journal-title":"Phys. Rev."},{"key":"ref_324","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1103\/PhysRev.156.630","article-title":"Interaction Range, The Goldstone Theorem, and Long-Range Order in the Heisenberg Ferromagnet","volume":"156","author":"Lange","year":"1967","journal-title":"Phys. Rev."},{"key":"ref_325","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1103\/PhysRevB.6.1891","article-title":"Critical Exponents in Isotropic Spin Systems","volume":"6","author":"Wegner","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_326","doi-asserted-by":"crossref","first-page":"052113","DOI":"10.1103\/PhysRevE.92.052113","article-title":"Fixed-point structure and effective fractional dimensionality for O(N) models with long-range interactions","volume":"92","author":"Defenu","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_327","doi-asserted-by":"crossref","first-page":"8","DOI":"10.21468\/SciPostPhysCore.7.1.008","article-title":"Deconfined quantum criticality in the long-range, anisotropic Heisenberg chain","volume":"7","author":"Romen","year":"2024","journal-title":"SciPost Phys. Core."},{"key":"ref_328","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1038\/s41586-023-06656-7","article-title":"Continuous symmetry breaking in a trapped-ion spin chain","volume":"623","author":"Feng","year":"2023","journal-title":"Nature"},{"key":"ref_329","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1038\/s41586-023-05859-2","article-title":"Continuous symmetry breaking in a two-dimensional Rydberg array","volume":"616","author":"Chen","year":"2023","journal-title":"Nature"},{"key":"ref_330","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1103\/PhysRevLett.60.635","article-title":"Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-12 antiferromagnetic Heisenberg chain with 1\/r2 exchange","volume":"60","author":"Haldane","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_331","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1103\/PhysRevLett.60.639","article-title":"Exact solution of an S=1\/2 Heisenberg antiferromagnetic chain with long-ranged interactions","volume":"60","author":"Shastry","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_332","doi-asserted-by":"crossref","first-page":"13357","DOI":"10.1103\/PhysRevB.51.13357","article-title":"Dressed S matrices in models with long-range interactions","volume":"51","year":"1995","journal-title":"Phys. Rev. B"},{"key":"ref_333","doi-asserted-by":"crossref","first-page":"107202","DOI":"10.1103\/PhysRevLett.121.107202","article-title":"Critical Level Crossings and Gapless Spin Liquid in the Square-Lattice Spin-1\/2J1\u2013J2 Heisenberg Antiferromagnet","volume":"121","author":"Wang","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_334","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1126\/science.1091806","article-title":"Deconfined Quantum Critical Points","volume":"303","author":"Senthil","year":"2004","journal-title":"Science"},{"key":"ref_335","doi-asserted-by":"crossref","first-page":"144407","DOI":"10.1103\/PhysRevB.70.144407","article-title":"Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm","volume":"70","author":"Senthil","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_336","doi-asserted-by":"crossref","first-page":"224416","DOI":"10.1103\/PhysRevB.69.224416","article-title":"Quantum criticality and deconfinement in phase transitions between valence bond solids","volume":"69","author":"Vishwanath","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_337","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1143\/JPSJS.74S.1","article-title":"Deconfined Criticality Critically Defined","volume":"74","author":"Senthil","year":"2005","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_338","unstructured":"Yang, S., Yao, D.X., and Sandvik, A.W. (2020). Deconfined quantum criticality in spin-1\/2 chains with long-range interactions. arXiv."},{"key":"ref_339","unstructured":"Adelhardt, P., and Schmidt, K.P. (2024). Raw data from the pCUT+MC approach for the antiferromagnetic Heisenberg square lattice bilayer model with (non-frustrating) long-range interactions. Zenodo."},{"key":"ref_340","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1143\/JPSJ.59.2230","article-title":"Low Temperature Properties of the Double Layer Quantum Heisenberg Antiferromagnet -Modified Spin Wave Method-","volume":"59","author":"Hida","year":"1990","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_341","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1143\/JPSJ.61.1013","article-title":"Quantum Disordered State without Frustration in the Double Layer Heisenberg Antiferromagnet\u2013Dimer Expansion and Projector Monte Carlo Study\u2013","volume":"61","author":"Hida","year":"1992","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_342","doi-asserted-by":"crossref","first-page":"2777","DOI":"10.1103\/PhysRevLett.72.2777","article-title":"Order-disorder transition in a two-layer quantum antiferromagnet","volume":"72","author":"Sandvik","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"ref_343","doi-asserted-by":"crossref","first-page":"16483","DOI":"10.1103\/PhysRevB.51.16483","article-title":"Quantum critical behavior in a two-layer antiferromagnet","volume":"51","author":"Sandvik","year":"1995","journal-title":"Phys. Rev. B"},{"key":"ref_344","doi-asserted-by":"crossref","first-page":"014431","DOI":"10.1103\/PhysRevB.73.014431","article-title":"High-precision finite-size scaling analysis of the quantum-critical point of S=1\/2 Heisenberg antiferromagnetic bilayers","volume":"73","author":"Wang","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_345","doi-asserted-by":"crossref","first-page":"127202","DOI":"10.1103\/PhysRevLett.101.127202","article-title":"Evidence for an Unconventional Universality Class from a Two-Dimensional Dimerized Quantum Heisenberg Model","volume":"101","author":"Wenzel","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_346","doi-asserted-by":"crossref","first-page":"245137","DOI":"10.1103\/PhysRevB.92.245137","article-title":"Dynamical structure factors and excitation modes of the bilayer Heisenberg model","volume":"92","author":"Coletta","year":"2015","journal-title":"Phys. Rev. B"},{"key":"ref_347","unstructured":"Coester, K. (2011). Series Expansions for Dimerized Quantum Spin Systems. [Ph.D. Thesis, TU Dortmund]."},{"key":"ref_348","doi-asserted-by":"crossref","first-page":"125136","DOI":"10.1103\/PhysRevB.84.125136","article-title":"Anisotropic perturbations in three-dimensional O(N)-symmetric vector models","volume":"84","author":"Hasenbusch","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_349","doi-asserted-by":"crossref","first-page":"105013","DOI":"10.1103\/PhysRevD.104.105013","article-title":"Bootstrapping Heisenberg magnets and their cubic instability","volume":"104","author":"Chester","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_350","doi-asserted-by":"crossref","first-page":"184413","DOI":"10.1103\/PhysRevB.67.184413","article-title":"Rung-singlet phase of the S = 12 two-leg spin-ladder with four-spin cyclic exchange","volume":"67","author":"Schmidt","year":"2003","journal-title":"Phys. Rev. B"},{"key":"ref_351","doi-asserted-by":"crossref","first-page":"3196","DOI":"10.1103\/PhysRevB.47.3196","article-title":"Excitation spectrum of Heisenberg spin ladders","volume":"47","author":"Barnes","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_352","doi-asserted-by":"crossref","first-page":"8521","DOI":"10.1103\/PhysRevB.53.8521","article-title":"Antiferromagnetic spin ladders: Crossover between spin S=1\/2 and S=1 chains","volume":"53","author":"Shelton","year":"1996","journal-title":"Phys. Rev. B"},{"key":"ref_353","doi-asserted-by":"crossref","unstructured":"Adelhardt, P., and Schmidt, K.P. (2023). Raw data to \u201cContinuously varying critical exponents in long-range quantum spin ladders\u201d. Zenodo.","DOI":"10.21468\/SciPostPhys.15.3.087"},{"key":"ref_354","doi-asserted-by":"crossref","first-page":"174421","DOI":"10.1103\/PhysRevB.98.174421","article-title":"Dynamical signature of fractionalization at a deconfined quantum critical point","volume":"98","author":"Ma","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_355","doi-asserted-by":"crossref","first-page":"227202","DOI":"10.1103\/PhysRevLett.98.227202","article-title":"Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions","volume":"98","author":"Sandvik","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_356","doi-asserted-by":"crossref","first-page":"017203","DOI":"10.1103\/PhysRevLett.100.017203","article-title":"Scaling in the Fan of an Unconventional Quantum Critical Point","volume":"100","author":"Melko","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_357","doi-asserted-by":"crossref","first-page":"P02009","DOI":"10.1088\/1742-5468\/2008\/02\/P02009","article-title":"From an antiferromagnet to a valence bond solid: Evidence for a first-order phase transition","volume":"2008","author":"Jiang","year":"2008","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_358","doi-asserted-by":"crossref","first-page":"180414","DOI":"10.1103\/PhysRevB.80.180414","article-title":"Antiferromagnetic to valence-bond-solid transitions in two-dimensional SU(N) Heisenberg models with multispin interactions","volume":"80","author":"Lou","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_359","doi-asserted-by":"crossref","first-page":"177201","DOI":"10.1103\/PhysRevLett.104.177201","article-title":"Continuous Quantum Phase Transition between an Antiferromagnet and a Valence-Bond Solid in Two Dimensions: Evidence for Logarithmic Corrections to Scaling","volume":"104","author":"Sandvik","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_360","doi-asserted-by":"crossref","first-page":"220408","DOI":"10.1103\/PhysRevB.88.220408","article-title":"Possibility of deconfined criticality in SU(N) Heisenberg models at small N","volume":"88","author":"Harada","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_361","doi-asserted-by":"crossref","first-page":"3123","DOI":"10.1143\/JPSJ.68.3123","article-title":"Mechanism of CDW-SDW Transition in One Dimension","volume":"68","author":"Nakamura","year":"1999","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_362","doi-asserted-by":"crossref","first-page":"16377","DOI":"10.1103\/PhysRevB.61.16377","article-title":"Tricritical behavior in the extended Hubbard chains","volume":"61","author":"Nakamura","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_363","doi-asserted-by":"crossref","first-page":"155113","DOI":"10.1103\/PhysRevB.65.155113","article-title":"Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model","volume":"65","author":"Sengupta","year":"2002","journal-title":"Phys. Rev. B"},{"key":"ref_364","doi-asserted-by":"crossref","first-page":"236401","DOI":"10.1103\/PhysRevLett.92.236401","article-title":"Ground State Phases of the Half-Filled One-Dimensional Extended Hubbard Model","volume":"92","author":"Sandvik","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_365","doi-asserted-by":"crossref","first-page":"035103","DOI":"10.1103\/PhysRevB.69.035103","article-title":"Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model","volume":"69","author":"Tsuchiizu","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_366","doi-asserted-by":"crossref","first-page":"075103","DOI":"10.1103\/PhysRevB.99.075103","article-title":"Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points","volume":"99","author":"Jiang","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_367","doi-asserted-by":"crossref","first-page":"165143","DOI":"10.1103\/PhysRevB.99.165143","article-title":"Deconfined quantum critical point in one dimension","volume":"99","author":"Roberts","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_368","doi-asserted-by":"crossref","first-page":"125137","DOI":"10.1103\/PhysRevB.100.125137","article-title":"Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point","volume":"100","author":"Huang","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_369","doi-asserted-by":"crossref","first-page":"075125","DOI":"10.1103\/PhysRevB.85.075125","article-title":"Symmetry protection of topological phases in one-dimensional quantum spin systems","volume":"85","author":"Pollmann","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_370","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1103\/PhysRevLett.55.1355","article-title":"Critical Behavior of Two-Dimensional Systems with Continuous Symmetries","volume":"55","author":"Affleck","year":"1985","journal-title":"Phys. Rev. Lett."},{"key":"ref_371","doi-asserted-by":"crossref","first-page":"5291","DOI":"10.1103\/PhysRevB.36.5291","article-title":"Critical theory of quantum spin chains","volume":"36","author":"Affleck","year":"1987","journal-title":"Phys. Rev. B"},{"key":"ref_372","doi-asserted-by":"crossref","first-page":"195301","DOI":"10.1103\/PhysRevLett.129.195301","article-title":"Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids","volume":"129","author":"Tarabunga","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_373","doi-asserted-by":"crossref","first-page":"174433","DOI":"10.1103\/PhysRevB.98.174433","article-title":"Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice","volume":"98","author":"Emonts","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_374","unstructured":"Patil, P. (2023). Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays. arXiv."},{"key":"ref_375","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1103\/RevModPhys.66.129","article-title":"Renormalization-group approach to interacting fermions","volume":"66","author":"Shankar","year":"1994","journal-title":"Rev. Mod. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/5\/401\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:38:21Z","timestamp":1760107101000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/5\/401"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,1]]},"references-count":375,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["e26050401"],"URL":"https:\/\/doi.org\/10.3390\/e26050401","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,1]]}}}