Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

Ayral, Thomas; Lee, Tsung-Han; Kotliar, Gabriel

doi:10.1103/PhysRevB.96.235139

Title: Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

Journal Article · Tue Dec 26 00:00:00 EST 2017 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.96.235139· OSTI ID:1425076

Ayral, Thomas ^[1]; Lee, Tsung-Han ^[1]; Kotliar, Gabriel ^[2]

Rutgers Univ., Piscataway, NJ (United States). Physics and Astronomy Dept.
Rutgers Univ., Piscataway, NJ (United States). Physics and Astronomy Dept.; Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.

In this paper, we present a unified perspective on dynamical mean-field theory (DMFT), density-matrix embedding theory (DMET), and rotationally invariant slave bosons (RISB). We show that DMET can be regarded as a simplification of the RISB method where the quasiparticle weight is set to unity. Finally, this relation makes it easy to transpose extensions of a given method to another: For instance, a temperature-dependent version of RISB can be used to derive a temperature-dependent free-energy formula for DMET.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012704; FG02-99ER45761

OSTI ID:: 1425076

Alternate ID(s):: OSTI ID: 1414852

Report Number(s):: BNL-203221-2018-JAAM; TRN: US1802033

Journal Information:: Physical Review B, Vol. 96, Issue 23; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 26 works

Citation information provided by
Web of Science

References (56)

Exact solution of the one-dimensional spin- $\frac{\mathsf 3}{\mathsf 2}$ Ising model in magnetic field Avella, A.; Mancini, F. The European Physical Journal B, Vol. 50, Issue 4 https://doi.org/10.1140/epjb/e2006-00177-x	journal	April 2006
New Functional Integral Approach to Strongly Correlated Fermi Systems: The Gutzwiller Approximation as a Saddle Point Kotliar, Gabriel; Ruckenstein, Andrei E. Physical Review Letters, Vol. 57, Issue 11 https://doi.org/10.1103/PhysRevLett.57.1362	journal	September 1986
Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory Knizia, Gerald; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct301044e	journal	February 2013
Electronic structure and core-level spectra of light actinide dioxides in the dynamical mean-field theory Kolorenč, Jindřich; Shick, Alexander B.; Lichtenstein, Alexander I. Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.085125	journal	August 2015
Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory Zheng, Bo-Xiao; Chan, Garnet Kin-Lic Physical Review B, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevB.93.035126	journal	January 2016
Dynamical mean-field theory for molecular electronics: Electronic structure and transport properties Jacob, D.; Haule, K.; Kotliar, G. Physical Review B, Vol. 82, Issue 19 https://doi.org/10.1103/PhysRevB.82.195115	journal	November 2010
Valence-band satellite in ferromagnetic nickel: LDA+DMFT study with exact diagonalization Kolorenč, Jindřich; Poteryaev, Alexander I.; Lichtenstein, Alexander I. Physical Review B, Vol. 85, Issue 23 https://doi.org/10.1103/PhysRevB.85.235136	journal	June 2012
Finite temperature quantum embedding theories for correlated systems Zgid, Dominika; Gull, Emanuel New Journal of Physics, Vol. 19, Issue 2 https://doi.org/10.1088/1367-2630/aa5d34	journal	February 2017
Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems Schiró, Marco; Fabrizio, Michele Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevLett.105.076401	journal	August 2010
Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space Ferrero, Michel; Cornaglia, Pablo S.; De Leo, Lorenzo Physical Review B, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevB.80.064501	journal	August 2009
Two-site dynamical mean-field theory Potthoff, Michael Physical Review B, Vol. 64, Issue 16 https://doi.org/10.1103/PhysRevB.64.165114	journal	October 2001
Quantum cluster theories Maier, Thomas; Jarrell, Mark; Pruschke, Thomas Reviews of Modern Physics, Vol. 77, Issue 3 https://doi.org/10.1103/RevModPhys.77.1027	journal	October 2005
Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory Knizia, Gerald; Chan, Garnet Kin-Lic Physical Review Letters, Vol. 109, Issue 18 https://doi.org/10.1103/PhysRevLett.109.186404	journal	November 2012
Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity Caffarel, Michel; Krauth, Werner Physical Review Letters, Vol. 72, Issue 10 https://doi.org/10.1103/PhysRevLett.72.1545	journal	March 1994
Time-dependent and steady-state Gutzwiller approach for nonequilibrium transport in nanostructures Lanatà, Nicola; Strand, Hugo U. R. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115310	journal	September 2012
Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver Zheng, Bo-Xiao; Kretchmer, Joshua S.; Shi, Hao Physical Review B, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevB.95.045103	journal	January 2017
Efficient implementation of the Gutzwiller variational method Lanatà, Nicola; Strand, Hugo U. R.; Dai, Xi Physical Review B, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevB.85.035133	journal	January 2012
Large-amplitude spin oscillations triggered by nonequilibrium strongly correlated $t_{2 g}$ electrons Behrmann, Malte; Lechermann, Frank Physical Review B, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevB.91.075110	journal	February 2015
Nonequilibrium superconductivity in driven alkali-doped fullerides Mazza, Giacomo; Georges, Antoine Physical Review B, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevB.96.064515	journal	August 2017
Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium Behrmann, Malte; Fabrizio, Michele; Lechermann, Frank Physical Review B, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevB.88.035116	journal	July 2013
Electronic transport and dynamics in correlated heterostructures Mazza, G.; Amaricci, A.; Capone, M. Physical Review B, Vol. 91, Issue 19 https://doi.org/10.1103/PhysRevB.91.195124	journal	May 2015
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions Georges, Antoine; Kotliar, Gabriel; Krauth, Werner Reviews of Modern Physics, Vol. 68, Issue 1 https://doi.org/10.1103/RevModPhys.68.13	journal	January 1996
Dynamical Mean-Field Theory for Quantum Chemistry Lin, Nan; Marianetti, C. A.; Millis, Andrew J. Physical Review Letters, Vol. 106, Issue 9 https://doi.org/10.1103/PhysRevLett.106.096402	journal	March 2011
Spectral Weight of the Hubbard Model through Cluster Perturbation Theory Sénéchal, D.; Perez, D.; Pioro-Ladrière, M. Physical Review Letters, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevLett.84.522	journal	January 2000
Self-energy-functional approach to systems of correlated electrons Potthoff, M. The European Physical Journal B - Condensed Matter, Vol. 32, Issue 4 https://doi.org/10.1140/epjb/e2003-00121-8	journal	April 2003
Rotationally invariant slave bosons for strongly correlated superconductors Isidori, A.; Capone, M. Physical Review B, Vol. 80, Issue 11 https://doi.org/10.1103/PhysRevB.80.115120	journal	September 2009
Mott transitions in the two-dimensional half-filled Hubbard model: Correlator projection method with projective dynamical mean-field approximation Onoda, Shigeki; Imada, Masatoshi Physical Review B, Vol. 67, Issue 16 https://doi.org/10.1103/PhysRevB.67.161102	journal	April 2003
Local density approximation in site-occupation embedding theory Senjean, Bruno; Tsuchiizu, Masahisa; Robert, Vincent Molecular Physics, Vol. 115, Issue 1-2 https://doi.org/10.1080/00268976.2016.1182224	journal	May 2016
Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations Schiró, Marco; Fabrizio, Michele Physical Review B, Vol. 83, Issue 16 https://doi.org/10.1103/PhysRevB.83.165105	journal	April 2011
Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum Mazza, Giacomo; Fabrizio, Michele Physical Review B, Vol. 86, Issue 18 https://doi.org/10.1103/PhysRevB.86.184303	journal	November 2012
On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation Fromager, Emmanuel Molecular Physics, Vol. 113, Issue 5 https://doi.org/10.1080/00268976.2014.993342	journal	August 2014
On the nature of the Mott transition in multiorbital systems Facio, Jorge I.; Vildosola, V.; García, D. J. Physical Review B, Vol. 95, Issue 8 https://doi.org/10.1103/PhysRevB.95.085119	journal	February 2017
Valence bond dynamical mean-field theory of doped Mott insulators with nodal/antinodal differentiation Ferrero, M.; Cornaglia, P. S.; De Leo, L. EPL (Europhysics Letters), Vol. 85, Issue 5 https://doi.org/10.1209/0295-5075/85/57009	journal	March 2009
Slave Boson Theory of Orbital Differentiation with Crystal Field Effects: Application to ${UO}_{2}$ Lanatà, Nicola; Yao, Yongxin; Deng, Xiaoyu Physical Review Letters, Vol. 118, Issue 12 https://doi.org/10.1103/PhysRevLett.118.126401	journal	March 2017
Cluster expansion for the self-energy: A simple many-body method for interpreting the photoemission spectra of correlated Fermi systems Gros, Claudius; Valentí, Roser Physical Review B, Vol. 48, Issue 1 https://doi.org/10.1103/PhysRevB.48.418	journal	July 1993
Theoretical prediction of a strongly correlated Dirac metal Mazin, I. I.; Jeschke, Harald O.; Lechermann, Frank Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5261	journal	July 2014
A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Sun, Qiming Journal of Chemical Theory and Computation, Vol. 12, Issue 6 https://doi.org/10.1021/acs.jctc.6b00316	journal	May 2016
Spectral functions of strongly correlated extended systems via an exact quantum embedding Booth, George H.; Chan, Garnet Kin-Lic Physical Review B, Vol. 91, Issue 15 https://doi.org/10.1103/PhysRevB.91.155107	journal	April 2015
Cellular Dynamical Mean Field Approach to Strongly Correlated Systems Biroli, Giulio; Kotliar, Gabriel; Pálsson, Gunnar The American Physical Society https://doi.org/10.17877/de290r-11153	text	January 2001
Quantum cluster theories Maier, Thomas; Jarrell, Mark; Pruschke, Thomas Karlsruhe https://doi.org/10.5445/ir/1000012189	text	January 2005
Valence-Bond Dynamical Mean-Field Theory of Doped Mott Insulators with Nodal/Antinodal Differentiation Ferrero, M.; Cornaglia, P. S.; De Leo, L. arXiv https://doi.org/10.48550/arxiv.0806.4383	text	January 2008
Dynamical Mean-Field Theory for Quantum Chemistry Lin, Nan; Marianetti, C. A.; Millis, Andrew J. arXiv https://doi.org/10.48550/arxiv.1010.3180	text	January 2010
Time-Dependent and Steady-State Gutzwiller approach for nonequilibrium transport in nanostructures Lanatà, Nicola; Strand, Hugo U. R. arXiv https://doi.org/10.48550/arxiv.1102.2741	text	January 2011
Valence-band satellite in the ferromagnetic nickel: LDA+DMFT study with exact diagonalization Kolorenc, Jindrich; Poteryaev, Alexander I.; Lichtenstein, Alexander I. arXiv https://doi.org/10.48550/arxiv.1202.6595	text	January 2012
Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum Mazza, Giacomo; Fabrizio, Michele arXiv https://doi.org/10.48550/arxiv.1210.2034	text	January 2012
Spectral functions of strongly correlated extended systems via an exact quantum embedding Booth, George H.; Chan, Garnet Kin-Lic arXiv https://doi.org/10.48550/arxiv.1309.2320	text	January 2013
Theoretical prediction of a strongly correlated Dirac metal Mazin, I. I.; Jeschke, Harald O.; Lechermann, Frank arXiv https://doi.org/10.48550/arxiv.1403.0616	text	January 2014
Large-amplitude spin oscillations triggered by nonequilibrium strongly correlated $t_{2g}$ electrons Behrmann, Malte; Lechermann, Frank arXiv https://doi.org/10.48550/arxiv.1404.6118	text	January 2014
On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation Fromager, Emmanuel arXiv https://doi.org/10.48550/arxiv.1409.2326	text	January 2014
Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory Zheng, Bo-Xiao; Chan, Garnet Kin-Lic arXiv https://doi.org/10.48550/arxiv.1504.01784	text	January 2015
Electronic structure and core-level spectra of light actinide dioxides in the dynamical mean-field theory Kolorenc, Jindrich; Shick, Alexander B.; Lichtenstein, Alexander I. arXiv https://doi.org/10.48550/arxiv.1504.07979	text	January 2015
A practical guide to density matrix embedding theory in quantum chemistry Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Sun, Qiming arXiv https://doi.org/10.48550/arxiv.1603.08443	text	January 2016
On the nature of the Mott transition in multiorbital systems Facio, Jorge I.; Vildosola, V.; García, D. J. arXiv https://doi.org/10.48550/arxiv.1605.08652	text	January 2016
Finite temperature quantum embedding theories for correlated systems Zgid, Dominika; Gull, Emanuel arXiv https://doi.org/10.48550/arxiv.1611.00395	text	January 2016
Two-site dynamical mean-field theory Potthoff, M. arXiv https://doi.org/10.48550/arxiv.cond-mat/0107502	text	January 2001
The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems Hettler, M. H.; Mukherjee, M.; Jarrell, M. arXiv https://doi.org/10.48550/arxiv.cond-mat/9903273	text	January 1999

Cited By (9)

Multiple impurities and combined local density approximations in site-occupation embedding theory Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa Theoretical Chemistry Accounts, Vol. 137, Issue 12 https://doi.org/10.1007/s00214-018-2368-z	journal	November 2018
Energy-weighted density matrix embedding of open correlated chemical fragments Fertitta, Edoardo; Booth, George H. The Journal of Chemical Physics, Vol. 151, Issue 1 https://doi.org/10.1063/1.5100290	journal	July 2019
Projected density matrix embedding theory with applications to the two-dimensional Hubbard model Wu, Xiaojie; Cui, Zhi-Hao; Tong, Yu The Journal of Chemical Physics, Vol. 151, Issue 6 https://doi.org/10.1063/1.5108818	journal	August 2019
Correlated materials design: prospects and challenges Adler, Ran; Kang, Chang-Jong; Yee, Chuck-Hou Reports on Progress in Physics, Vol. 82, Issue 1 https://doi.org/10.1088/1361-6633/aadca4	journal	December 2018
Rigorous wave function embedding with dynamical fluctuations Fertitta, Edoardo; Booth, George H. Physical Review B, Vol. 98, Issue 23 https://doi.org/10.1103/physrevb.98.235132	journal	December 2018
Toward a predictive theory of correlated materials Kent, Paul R. C.; Kotliar, Gabriel Science, Vol. 361, Issue 6400 https://doi.org/10.1126/science.aat5975	journal	July 2018
Correlated materials design: prospects and challenges Adler, Ran; Kang, Chang-Jong; Yee, Chuck-Hou arXiv https://doi.org/10.48550/arxiv.1807.00398	text	January 2018
Rigorous wave function embedding with dynamical fluctuations Fertitta, Edoardo; Booth, George H. arXiv https://doi.org/10.48550/arxiv.1808.09321	text	January 2018
Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions Dvorak, Marc; Rinke, Patrick arXiv https://doi.org/10.48550/arxiv.1810.12009	text	January 2018

Similar Records

Rotationally invariant slave-boson and density matrix embedding theory: Unified framework and comparative study on the one-dimensional and two-dimensional Hubbard model [Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model]

Journal Article · Fri Mar 15 00:00:00 EDT 2019 · Physical Review B · OSTI ID:1425076

Lee, Tsung -Han; Ayral, Thomas; Yao, Yong -Xin; +2 more

Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Journal Article · Mon Dec 09 00:00:00 EST 2019 · Journal of Chemical Theory and Computation · OSTI ID:1425076

Pham, Hung Q.; Hermes, Matthew R.; Gagliardi, Laura

Slave-boson mean-field theory of the antiferromagnetic state in the doubly degenerate Hubbard model: The half-filled case

Journal Article · Tue Jul 01 00:00:00 EDT 1997 · Physical Review, B: Condensed Matter · OSTI ID:1425076

Hasegawa, H

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY

Title: Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

Citation Formats

References (56)

Cited By (9)

Similar Records

Related Subjects