{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:34:47Z","timestamp":1760150087490,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T00:00:00Z","timestamp":1696982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"ANR","doi-asserted-by":"publisher","award":["ANR-19CE29-0002 DESCARTES"],"award-info":[{"award-number":["ANR-19CE29-0002 DESCARTES"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The performance of embedding methods is directly tied to the quality of the bath orbital construction. In this paper, we develop a versatile framework, enabling the investigation of the optimal construction of the orbitals of the bath. As of today, in state-of-the-art embedding methods, the orbitals of the bath are constructed by performing a Singular Value Decomposition (SVD) on the impurity-environment part of the one-body reduced density matrix, as originally presented in Density Matrix Embedding Theory. Recently, the equivalence between the SVD protocol and the use of unitary transformation, the so-called Block-Householder transformation, has been established. We present a generalization of the Block-Householder transformation by introducing additional flexible parameters. The additional parameters are optimized such that the bath-orbitals fulfill physically motivated constraints. The efficiency of the approach is discussed and exemplified in the context of the half-filled Hubbard model in one-dimension.<\/jats:p>","DOI":"10.3390\/computation11100203","type":"journal-article","created":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T03:07:47Z","timestamp":1697080067000},"page":"203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Versatile Unitary Transformation Framework for an Optimal Bath Construction in Density-Matrix Based Quantum Embedding Approaches"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8907-7666","authenticated-orcid":false,"given":"Quentin","family":"Mar\u00e9cat","sequence":"first","affiliation":[{"name":"ICGM, Universit\u00e9 de Montpellier, CNRS, ENSCM, 34000 Montpellier, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9900-6175","authenticated-orcid":false,"given":"Matthieu","family":"Sauban\u00e8re","sequence":"additional","affiliation":[{"name":"ICGM, Universit\u00e9 de Montpellier, CNRS, ENSCM, 34000 Montpellier, France"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2705","DOI":"10.1021\/acs.accounts.6b00356","article-title":"Quantum Embedding Theories","volume":"49","author":"Sun","year":"2016","journal-title":"Acc. Chem. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e26495","DOI":"10.1002\/qua.26495","article-title":"Quantum embedding electronic structure methods","volume":"120","author":"Wasserman","year":"2020","journal-title":"Int. J. Quantum Chem."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"186401","DOI":"10.1103\/PhysRevLett.87.186401","article-title":"Cellular Dynamical Mean Field Approach to Strongly Correlated Systems","volume":"87","author":"Kotliar","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"14868","DOI":"10.1103\/PhysRevB.48.14868","article-title":"Self-consistent cluster-embedding calculation method and the calculated electronic structure of NiO","volume":"48","author":"Zheng","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2116","DOI":"10.1021\/acs.jctc.0c01258","article-title":"Quantum embedding theory for strongly correlated states in materials","volume":"17","author":"Ma","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1126\/science.1158722","article-title":"Insights into Current Limitations of Density Functional Theory","volume":"321","author":"Cohen","year":"2008","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"150901","DOI":"10.1063\/1.4704546","article-title":"Perspective on density functional theory","volume":"136","author":"Burke","year":"2012","journal-title":"J. Chem. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/BF01311397","article-title":"Correlated fermions on a lattice in high dimensions","volume":"74","year":"1989","journal-title":"Z. F\u00fcr Phys. B Condens. Matter"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1103\/RevModPhys.68.13","article-title":"Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions","volume":"68","author":"Georges","year":"1996","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6479","DOI":"10.1103\/PhysRevB.45.6479","article-title":"Hubbard model in infinite dimensions","volume":"45","author":"Georges","year":"1992","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1103\/PhysRev.124.41","article-title":"Localized magnetic states in metals","volume":"124","author":"Anderson","year":"1961","journal-title":"Phys. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1140\/epjb\/e2003-00121-8","article-title":"Self-energy-functional approach to systems of correlated electrons","volume":"32","author":"Potthoff","year":"2003","journal-title":"Eur. Phys. J. B"},{"key":"ref_13","first-page":"L667","article-title":"A new functional integral formalism for strongly correlated fermi systems","volume":"21","author":"Sarker","year":"1988","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"195104","DOI":"10.1103\/PhysRevB.100.195104","article-title":"Site-occupation Green\u2019s function embedding theory: A density functional approach to dynamical impurity solvers","volume":"100","author":"Mazouin","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4856","DOI":"10.1021\/acs.jctc.6b00638","article-title":"Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green\u2019s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy","volume":"12","author":"Kananenka","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1038\/s43588-021-00090-3","article-title":"Maximally Localized Dynamical Quantum Embedding for Solving Many-Body Correlated Systems","volume":"1","author":"Lupo","year":"2021","journal-title":"Nat. Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lanat\u00e0, N. (2023). Derivation of the Ghost Gutzwiller Approximation from Quantum Embedding principles: The Ghost Density Matrix Embedding Theory. arXiv.","DOI":"10.1103\/PhysRevB.108.235112"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"035136","DOI":"10.1103\/PhysRevB.100.035136","article-title":"Projected site-occupation embedding theory","volume":"100","author":"Senjean","year":"2019","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Sekaran, S., Sauban\u00e8re, M., and Fromager, E. (2022). Local potential functional embedding theory: A self-consistent flavor of density functional theory for lattices without density functionals. Computation, 10.","DOI":"10.3390\/computation10030045"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3498","DOI":"10.1021\/acs.jctc.3c00247","article-title":"Density matrix embedding using multiconfiguration pair-density functional theory","volume":"19","author":"Mitra","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"186404","DOI":"10.1103\/PhysRevLett.109.186404","article-title":"Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory","volume":"109","author":"Knizia","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2706","DOI":"10.1021\/acs.jctc.6b00316","article-title":"A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry","volume":"12","author":"Wouters","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"214112","DOI":"10.1063\/5.0125683","article-title":"Quantum embedding of multi-orbital fragments using the block-Householder transformation","volume":"157","author":"Yalouz","year":"2022","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"034107","DOI":"10.1063\/5.0157746","article-title":"A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation","volume":"159","author":"Sekaran","year":"2023","journal-title":"J. Chem. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"235139","DOI":"10.1103\/PhysRevB.96.235139","article-title":"Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective","volume":"96","author":"Ayral","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_26","unstructured":"Canc\u00e8s, E., Faulstich, F., Kirsch, A., Letournel, E., and Levitt, A. (2023). Some mathematical insights on Density Matrix Embedding Theory. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"075131","DOI":"10.1103\/PhysRevB.101.075131","article-title":"Finite-temperature density matrix embedding theory","volume":"101","author":"Sun","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"194108","DOI":"10.1063\/1.5053992","article-title":"Incremental embedding: A density matrix embedding scheme for molecules","volume":"149","author":"Ye","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1021\/acs.jctc.8b01009","article-title":"Multiconfigurational Self-Consistent Field Theory with Density Matrix Embedding: The Localized Active Space Self-Consistent Field Method","volume":"15","author":"Hermes","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"035121","DOI":"10.1103\/PhysRevB.104.035121","article-title":"Householder-transformed density matrix functional embedding theory","volume":"104","author":"Sekaran","year":"2021","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1098\/rspa.1963.0204","article-title":"Electron correlations in narrow energy bands","volume":"276","author":"Hubbard","year":"1963","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Mar\u00e9cat, Q., Lasorne, B., Fromager, E., and Sauban\u00e8re, M. (2023). Unitary transformations within density matrix embedding approaches: A novel perspective on the self-consistent scheme for electronic structure calculation. arXiv.","DOI":"10.1103\/PhysRevB.108.155119"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"235101","DOI":"10.1103\/PhysRevB.83.235101","article-title":"Lattice density functional theory of the single-impurity Anderson model: Development and applications","volume":"83","author":"Pastor","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"245131","DOI":"10.1103\/PhysRevB.97.245131","article-title":"Adaptive cluster approximation for reduced density-matrix functional theory","volume":"97","author":"Schade","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0893-9659(99)00028-2","article-title":"Block Householder transformation for parallel QR factorization","volume":"12","author":"Rotella","year":"1999","journal-title":"Appl. Math. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1103\/PhysRevLett.72.1545","article-title":"Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity","volume":"72","author":"Caffarel","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1103\/PhysRevLett.20.1445","article-title":"Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension","volume":"20","author":"Lieb","year":"1968","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.1103\/PhysRevB.41.2326","article-title":"Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model","volume":"41","author":"Ogata","year":"1990","journal-title":"Phys. Rev. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. 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