Projected density matrix embedding theory with applications to the two-dimensional Hubbard model

Wu, Xiaojie; Cui, Zhi-Hao; Tong, Yu; Lindsey, Michael; Chan, Garnet Kin-Lic; Lin, Lin

doi:10.1063/1.5108818

Title: Projected density matrix embedding theory with applications to the two-dimensional Hubbard model

Abstract

Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency, especially for heterogeneous systems of large size. We introduce a new approach, called projected DMET (p-DMET), which achieves self-consistency without needing to optimize the correlation potential. We demonstrate the performance of p-DMET on the two-dimensional Hubbard model.

Authors:

Wu, Xiaojie ^[1]; Cui, Zhi-Hao ^[2]; Tong, Yu ^[1]; Lindsey, Michael ^[1]; Chan, Garnet Kin-Lic ^[2];

^[3]

Univ. of California, Berkeley, CA (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:: 2019-08-09

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)

OSTI Identifier:: 1572045

Alternate Identifier(s):: OSTI ID: 1549983

Grant/Contract Number:: AC02-05CH11231; SC0017867; CAMERA

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 151; Journal Issue: 6; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    Wu, Xiaojie, Cui, Zhi-Hao, Tong, Yu, Lindsey, Michael, Chan, Garnet Kin-Lic, and Lin, Lin. Projected density matrix embedding theory with applications to the two-dimensional Hubbard model.  United States: N. p., 2019. 
        Web.  doi:10.1063/1.5108818.

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                    Wu, Xiaojie, Cui, Zhi-Hao, Tong, Yu, Lindsey, Michael, Chan, Garnet Kin-Lic, & Lin, Lin. Projected density matrix embedding theory with applications to the two-dimensional Hubbard model.  United States.  doi:https://doi.org/10.1063/1.5108818

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                    Wu, Xiaojie, Cui, Zhi-Hao, Tong, Yu, Lindsey, Michael, Chan, Garnet Kin-Lic, and Lin, Lin. Fri .  
        "Projected density matrix embedding theory with applications to the two-dimensional Hubbard model".  United States.  doi:https://doi.org/10.1063/1.5108818.  https://www.osti.gov/servlets/purl/1572045.

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@article{osti_1572045,

  title        = {Projected density matrix embedding theory with applications to the two-dimensional Hubbard model},

  author       = {Wu, Xiaojie and Cui, Zhi-Hao and Tong, Yu and Lindsey, Michael and Chan, Garnet Kin-Lic and Lin, Lin},

  abstractNote = {Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency, especially for heterogeneous systems of large size. We introduce a new approach, called projected DMET (p-DMET), which achieves self-consistency without needing to optimize the correlation potential. We demonstrate the performance of p-DMET on the two-dimensional Hubbard model.},

  doi          = {10.1063/1.5108818},

  journal      = {Journal of Chemical Physics},

  number       = 6,

  volume       = 151,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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DOI: https://doi.org/10.1063/1.5108818

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Works referenced in this record:

Passing the one-billion limit in full configuration-interaction (FCI) calculations
journal, June 1990

Olsen, Jeppe; Jørgensen, Poul; Simons, Jack
Chemical Physics Letters, Vol. 169, Issue 6
DOI: 10.1016/0009-2614(90)85633-n

An algorithm for large scale density matrix renormalization group calculations
journal, February 2004

Chan, Garnet Kin-Lic
The Journal of Chemical Physics, Vol. 120, Issue 7
DOI: 10.1063/1.1638734

Convergence acceleration of iterative sequences. the case of scf iteration
journal, July 1980

Pulay, Péter
Chemical Physics Letters, Vol. 73, Issue 2
DOI: 10.1016/0009-2614(80)80396-4

Quantum Embedding Theories
journal, November 2016

Sun, Qiming; Chan, Garnet Kin-Lic
Accounts of Chemical Research, Vol. 49, Issue 12
DOI: 10.1021/acs.accounts.6b00356

P y SCF: the Python-based simulations of chemistry framework : The PySCF program
journal, September 2017

Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S.
Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1
DOI: 10.1002/wcms.1340

Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory
journal, February 2013

Knizia, Gerald; Chan, Garnet Kin-Lic
Journal of Chemical Theory and Computation, Vol. 9, Issue 3
DOI: 10.1021/ct301044e

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
journal, March 2002

Chan, Garnet Kin-Lic; Head-Gordon, Martin
The Journal of Chemical Physics, Vol. 116, Issue 11
DOI: 10.1063/1.1449459

The ab-initio density matrix renormalization group in practice
journal, January 2015

Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki
The Journal of Chemical Physics, Vol. 142, Issue 3
DOI: 10.1063/1.4905329

A new determinant-based full configuration interaction method
journal, November 1984

Knowles, P. J.; Handy, N. C.
Chemical Physics Letters, Vol. 111, Issue 4-5
DOI: 10.1016/0009-2614(84)85513-x

Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
journal, April 2014

Chen, Qiaoni; Booth, George H.; Sharma, Sandeep
Physical Review B, Vol. 89, Issue 16
DOI: 10.1103/physrevb.89.165134

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015

LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
Physical Review X, Vol. 5, Issue 4
DOI: 10.1103/physrevx.5.041041

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

Georges, Antoine; Kotliar, Gabriel; Krauth, Werner
Reviews of Modern Physics, Vol. 68, Issue 1
DOI: 10.1103/revmodphys.68.13

Density matrix embedding from broken symmetry lattice mean fields
journal, January 2014

Bulik, Ireneusz W.; Scuseria, Gustavo E.; Dukelsky, Jorge
Physical Review B, Vol. 89, Issue 3
DOI: 10.1103/physrevb.89.035140

Block product density matrix embedding theory for strongly correlated spin systems
journal, May 2017

Gunst, Klaas; Wouters, Sebastian; De Baerdemacker, Stijn
Physical Review B, Vol. 95, Issue 19
DOI: 10.1103/physrevb.95.195127

Density matrix embedding in an antisymmetrized geminal power bath
journal, July 2015

Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy
The Journal of Chemical Physics, Vol. 143, Issue 2
DOI: 10.1063/1.4926650

Spin-adapted density matrix renormalization group algorithms for quantum chemistry
journal, March 2012

Sharma, Sandeep; Chan, Garnet Kin-Lic
The Journal of Chemical Physics, Vol. 136, Issue 12
DOI: 10.1063/1.3695642

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory
journal, November 2012

Knizia, Gerald; Chan, Garnet Kin-Lic
Physical Review Letters, Vol. 109, Issue 18
DOI: 10.1103/physrevlett.109.186404

Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
journal, February 2018

Pham, Hung Q.; Bernales, Varinia; Gagliardi, Laura
Journal of Chemical Theory and Computation, Vol. 14, Issue 4
DOI: 10.1021/acs.jctc.7b01248

Ground-state energy and spin gap of spin- $\frac{1}{2}$ Kagomé-Heisenberg antiferromagnetic clusters: Large-scale exact diagonalization results
journal, June 2011

Läuchli, Andreas M.; Sudan, Julien; Sørensen, Erik S.
Physical Review B, Vol. 83, Issue 21
DOI: 10.1103/physrevb.83.212401

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations
journal, November 2017

Vogiatzis, Konstantinos D.; Ma, Dongxia; Olsen, Jeppe
The Journal of Chemical Physics, Vol. 147, Issue 18
DOI: 10.1063/1.4989858

Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems
journal, November 2010

Imada, Masatoshi; Miyake, Takashi
Journal of the Physical Society of Japan, Vol. 79, Issue 11
DOI: 10.1143/jpsj.79.112001

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations
journal, October 2017

Hu, Wei; Lin, Lin; Yang, Chao
Journal of Chemical Theory and Computation, Vol. 13, Issue 11
DOI: 10.1021/acs.jctc.7b00892

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
journal, January 2016

Zheng, Bo-Xiao; Chan, Garnet Kin-Lic
Physical Review B, Vol. 93, Issue 3
DOI: 10.1103/physrevb.93.035126

Cluster density matrix embedding theory for quantum spin systems
journal, May 2015

Fan, Zhuo; Jie, Quan-lin
Physical Review B, Vol. 91, Issue 19
DOI: 10.1103/physrevb.91.195118

Numerical solution of the d =∞ Hubbard model: Evidence for a Mott transition
journal, August 1992

Georges, Antoine; Krauth, Werner
Physical Review Letters, Vol. 69, Issue 8
DOI: 10.1103/physrevlett.69.1240

The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011

Chan, Garnet Kin-Lic; Sharma, Sandeep
Annual Review of Physical Chemistry, Vol. 62, Issue 1
DOI: 10.1146/annurev-physchem-032210-103338

Density-matrix algorithms for quantum renormalization groups
journal, October 1993

White, Steven R.
Physical Review B, Vol. 48, Issue 14
DOI: 10.1103/physrevb.48.10345

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver
journal, January 2017

Zheng, Bo-Xiao; Kretchmer, Joshua S.; Shi, Hao
Physical Review B, Vol. 95, Issue 4
DOI: 10.1103/physrevb.95.045103

Correlated Lattice Fermions in $d = \infty$ Dimensions
journal, January 1989

Metzner, Walter; Vollhardt, Dieter
Physical Review Letters, Vol. 62, Issue 3
DOI: 10.1103/physrevlett.62.324

Density matrix formulation for quantum renormalization groups
journal, November 1992

White, Steven R.
Physical Review Letters, Vol. 69, Issue 19
DOI: 10.1103/physrevlett.69.2863

Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017

Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe
Science, Vol. 358, Issue 6367
DOI: 10.1126/science.aam7127

Exact diagonalization of quantum-spin models
journal, October 1990

Lin, H. Q.
Physical Review B, Vol. 42, Issue 10
DOI: 10.1103/physrevb.42.6561

Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective
journal, December 2017

Ayral, Thomas; Lee, Tsung-Han; Kotliar, Gabriel
Physical Review B, Vol. 96, Issue 23
DOI: 10.1103/physrevb.96.235139

A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry
journal, May 2016

Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Sun, Qiming
Journal of Chemical Theory and Computation, Vol. 12, Issue 6
DOI: 10.1021/acs.jctc.6b00316

Electronic structure calculations with dynamical mean-field theory
journal, August 2006

Kotliar, G.; Savrasov, S. Y.; Haule, K.
Reviews of Modern Physics, Vol. 78, Issue 3
DOI: 10.1103/revmodphys.78.865

Correlated Lattice Fermions in $d = \infty$ Dimensions
journal, February 1989

Metzner, Walter; Vollhardt, Dieter
Physical Review Letters, Vol. 62, Issue 9
DOI: 10.1103/physrevlett.62.1066.2

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Title: Projected density matrix embedding theory with applications to the two-dimensional Hubbard model

Abstract

Citation Formats

Passing the one-billion limit in full configuration-interaction (FCI) calculations journal, June 1990

An algorithm for large scale density matrix renormalization group calculations journal, February 2004

Convergence acceleration of iterative sequences. the case of scf iteration journal, July 1980

Quantum Embedding Theories journal, November 2016

P y SCF: the Python-based simulations of chemistry framework : The PySCF program journal, September 2017

Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory journal, February 2013

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group journal, March 2002

The ab-initio density matrix renormalization group in practice journal, January 2015

A new determinant-based full configuration interaction method journal, November 1984

Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model journal, April 2014

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms journal, December 2015

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions journal, January 1996

Density matrix embedding from broken symmetry lattice mean fields journal, January 2014

Block product density matrix embedding theory for strongly correlated spin systems journal, May 2017

Density matrix embedding in an antisymmetrized geminal power bath journal, July 2015

Spin-adapted density matrix renormalization group algorithms for quantum chemistry journal, March 2012

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory journal, November 2012

Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems? journal, February 2018

Ground-state energy and spin gap of spin- 1 2 Kagomé-Heisenberg antiferromagnetic clusters: Large-scale exact diagonalization results journal, June 2011

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations journal, November 2017

Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems journal, November 2010

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations journal, October 2017

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory journal, January 2016

Cluster density matrix embedding theory for quantum spin systems journal, May 2015

Numerical solution of the d =∞ Hubbard model: Evidence for a Mott transition journal, August 1992

The Density Matrix Renormalization Group in Quantum Chemistry journal, May 2011

Density-matrix algorithms for quantum renormalization groups journal, October 1993

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver journal, January 2017

Correlated Lattice Fermions in d = ∞ Dimensions journal, January 1989

Density matrix formulation for quantum renormalization groups journal, November 1992

Stripe order in the underdoped region of the two-dimensional Hubbard model journal, November 2017

Exact diagonalization of quantum-spin models journal, October 1990

Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective journal, December 2017

A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry journal, May 2016

Electronic structure calculations with dynamical mean-field theory journal, August 2006

Correlated Lattice Fermions in d = ∞ Dimensions journal, February 1989

Passing the one-billion limit in full configuration-interaction (FCI) calculations
journal, June 1990

An algorithm for large scale density matrix renormalization group calculations
journal, February 2004

Convergence acceleration of iterative sequences. the case of scf iteration
journal, July 1980

Quantum Embedding Theories
journal, November 2016

P y SCF: the Python-based simulations of chemistry framework : The PySCF program
journal, September 2017

Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory
journal, February 2013

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
journal, March 2002

The ab-initio density matrix renormalization group in practice
journal, January 2015

A new determinant-based full configuration interaction method
journal, November 1984

Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
journal, April 2014

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

Density matrix embedding from broken symmetry lattice mean fields
journal, January 2014

Block product density matrix embedding theory for strongly correlated spin systems
journal, May 2017

Density matrix embedding in an antisymmetrized geminal power bath
journal, July 2015

Spin-adapted density matrix renormalization group algorithms for quantum chemistry
journal, March 2012

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory
journal, November 2012

Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
journal, February 2018

Ground-state energy and spin gap of spin- $\frac{1}{2}$ Kagomé-Heisenberg antiferromagnetic clusters: Large-scale exact diagonalization results
journal, June 2011

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations
journal, November 2017

Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems
journal, November 2010

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations
journal, October 2017

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
journal, January 2016

Cluster density matrix embedding theory for quantum spin systems
journal, May 2015

Numerical solution of the d =∞ Hubbard model: Evidence for a Mott transition
journal, August 1992

The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011

Density-matrix algorithms for quantum renormalization groups
journal, October 1993

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver
journal, January 2017

Correlated Lattice Fermions in $d = \infty$ Dimensions
journal, January 1989

Density matrix formulation for quantum renormalization groups
journal, November 1992

Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017

Exact diagonalization of quantum-spin models
journal, October 1990

Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective
journal, December 2017

A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry
journal, May 2016

Electronic structure calculations with dynamical mean-field theory
journal, August 2006

Correlated Lattice Fermions in $d = \infty$ Dimensions
journal, February 1989