{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:03:04Z","timestamp":1766268184291,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,18]],"date-time":"2019-02-18T00:00:00Z","timestamp":1550448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Crystals"],"abstract":"<jats:p>Quantum discord and entanglement are both criteria for distinguishing quantum correlations in a quantum system. We studied the effect of the transverse magnetic field on the quantum discord of the one-dimensional spin-1\/2 XX model. This study focused on the pair of spins at different distances. We show that quantum discord is finite for all studied spin pairs in the Luttinger liquid phase. In addition, relying on our calculations, we show that the derivatives of quantum discord can be used to identify the border between entangled and separable regions in the Luttinger liquid phase.<\/jats:p>","DOI":"10.3390\/cryst9020105","type":"journal-article","created":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T04:08:20Z","timestamp":1550549300000},"page":"105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Identification of Unentangled\u2013Entangled Border in the Luttinger Liquid Phase"],"prefix":"10.3390","volume":"9","author":[{"given":"Somayyeh","family":"Nemati","sequence":"first","affiliation":[{"name":"Beijing Computational Science Research Center, Beijing 100193, China"},{"name":"Center of Physics, University of Minho and University of Porto, P-4169-007 Oporto, Portugal"}]},{"given":"Fatemeh","family":"Khastehdel Fumani","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Guilan, Rasht 41335-1914, Iran"},{"name":"Department of Basic Sciences, Langaroud branch, Islamic Azad University, Langaroud 44713-11127, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2585-9439","authenticated-orcid":false,"given":"Saeed","family":"Mahdavifar","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Guilan, Rasht 41335-1914, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1103\/PhysRevLett.80.2245","article-title":"Entanglement of formation of an arbitrary state of two Qubits","volume":"80","author":"Wootters","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1038\/35005001","article-title":"Quantum information and computation","volume":"404","author":"Bennett","year":"2000","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1103\/RevModPhys.80.517","article-title":"Entanglement in many-body Systems","volume":"80","author":"Amico","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"017901","DOI":"10.1103\/PhysRevLett.88.017901","article-title":"Quantum discord: A measure of the quantum- ness of correlations","volume":"88","author":"Ollivier","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6899","DOI":"10.1088\/0305-4470\/34\/35\/315","article-title":"Classical quantum and total correlations","volume":"34","author":"Henderson","year":"2001","journal-title":"J. Phys. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"197901","DOI":"10.1103\/PhysRevLett.89.197901","article-title":"Quantum communication complexity protocol with two entangled qutrits","volume":"89","author":"Brukner","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1038\/nphys2377","article-title":"Quantum discord as resource for remote state preparation","volume":"8","author":"Lipp","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"140604","DOI":"10.1103\/PhysRevLett.96.140604","article-title":"Decay of Loschmidt echo enhanced by quantum criticality","volume":"96","author":"Quan","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"10007","DOI":"10.1209\/0295-5075\/111\/10007","article-title":"Gapped quantum criticality gains long-time quantum correlations","volume":"111","author":"Jafari","year":"2015","journal-title":"Europhys. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"042306","DOI":"10.1103\/PhysRevA.89.042306","article-title":"Induced effects of the dzyaloshinskii- moriya interaction on the thermal entanglement in spin-1\/2 Heisenberg chains","volume":"89","author":"Mehran","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1038\/nature01888","article-title":"Entangled quantum state of magnetic dipoles","volume":"425","author":"Ghosh","year":"2003","journal-title":"Nature"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1038\/425028a","article-title":"Quantum physics: Entanglement hits the big time","volume":"425","author":"Vedral","year":"2003","journal-title":"Nature"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1088\/1367-2630\/7\/1\/258","article-title":"Magnetic susceptibility as a macroscopic entanglement witness","volume":"7","author":"Wiesniak","year":"2005","journal-title":"New J. Phys."},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1038\/nphys3186","article-title":"Experimental realization of long-distance entanglement between spins in antiferromagnetic quantum spin chains","volume":"11","author":"Sahling","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1103\/PhysRevA.57.120","article-title":"Quantum computation with quantum dots","volume":"57","author":"Loss","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2070","DOI":"10.1103\/PhysRevB.59.2070","article-title":"Coupled quantum dots as quantum gates","volume":"59","author":"Burkard","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"032318","DOI":"10.1103\/PhysRevA.68.032318","article-title":"Entanglement and correlation in anisotropic quantum spin systems","volume":"68","author":"Glaser","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1103\/RevModPhys.70.897","article-title":"Magnetic, transport, and optical properties of monolayer copper oxides","volume":"70","author":"Kastner","year":"1998","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3651","DOI":"10.1103\/PhysRevLett.70.3651","article-title":"Observation of the spin-Peierls transition in linear Cu2+(spin-1\/2) chains in an inorganic compound CuGeO3","volume":"70","author":"Hase","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.physb.2004.03.064","article-title":"Incommensurate antiferromagnetic order in the S=1\/2 quantum chain compound LiCuVO4","volume":"350","author":"Gibson","year":"2004","journal-title":"Phys. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0378-4363(78)90108-0","article-title":"Field-induced magnetic ordering in the S = 1 singlet ground-state system Ni(C5H5NO)6(ClO4)2 studied by specific heat","volume":"93","author":"Algra","year":"1978","journal-title":"Phys. B+C"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/0378-4363(75)90001-7","article-title":"The specific heat of magnetic linear chains","volume":"79","author":"Blote","year":"1975","journal-title":"Phys. B+C"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"012014","DOI":"10.1088\/1742-6596\/143\/1\/012014","article-title":"Spin chain under next nearest neighbor interaction","volume":"143","author":"Kwek","year":"2009","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4204","DOI":"10.1103\/PhysRevLett.83.4204","article-title":"Quantum information processing using dot spins and cavity QED","volume":"83","author":"Imamog","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5188","DOI":"10.1103\/PhysRevLett.86.5188","article-title":"A one-way quantum computer","volume":"86","author":"Raussendorf","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"012313","DOI":"10.1103\/PhysRevA.64.012313","article-title":"Entanglement in the quantum Heisenberg XY model","volume":"64","author":"Wang","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.physa.2015.11.004","article-title":"Magnetic entanglement in spin-1\/2 xy chains","volume":"445","author":"Fumani","year":"2016","journal-title":"Phys. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"012323","DOI":"10.1103\/PhysRevA.80.012323","article-title":"Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields","volume":"80","author":"Gong","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"054410","DOI":"10.1103\/PhysRevB.89.054410","article-title":"Scaling of quantum discord in spin models","volume":"89","author":"Huang","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1143\/PTPS.157.164","article-title":"Ground state entanglement in spin systems","volume":"157","author":"Yano","year":"2005","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"032110","DOI":"10.1103\/PhysRevA.66.032110","article-title":"Entanglement in a simple quantum phase transition","volume":"66","author":"Osborne","year":"2002","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"012106","DOI":"10.1103\/PhysRevA.82.012106","article-title":"Quantum and classical thermal correlations in the xy spin-1\/2 chain","volume":"82","author":"Maziero","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.physa.2018.11.062","article-title":"Long range quantum coherence, quantum and classical correlations in Heisenberg XX chain","volume":"518","author":"Mzaouali","year":"2019","journal-title":"Phys. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"022315","DOI":"10.1103\/PhysRevA.96.022315","article-title":"Probabilistic quantum teleportation via thermal entanglement","volume":"96","author":"Fortes","year":"2017","journal-title":"Phy. Rev. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1007\/BF01331938","article-title":"About the Pauli exclusion principle","volume":"47","author":"Jordan","year":"1928","journal-title":"Z. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"032317","DOI":"10.1103\/PhysRevA.72.032317","article-title":"Quantum, classical, and total amount of correlations in a quantum state","volume":"72","author":"Groisman","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"022108","DOI":"10.1103\/PhysRevA.80.022108","article-title":"Classical correlation and quantum discord in critical systems","volume":"80","author":"Sarandy","year":"2009","journal-title":"Phys. Rev. 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