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

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Cited by: 4 works

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Figures / Tables:

FIG. 1: Illustration of a DMET 2-by-2 fragment embedded in a two-dimensional square lattice.

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Works referenced in this record:

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

Abstract

Citation Formats

Figures / Tables:

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

The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model text, January 2014

A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry text, January 2014

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory text, January 2015

A practical guide to density matrix embedding theory in quantum chemistry text, January 2016

Quantum embedding theories text, January 2016

Stripe order in the underdoped region of the two-dimensional Hubbard model text, January 2017

Block product density matrix embedding theory for strongly correlated spin systems text, January 2017

Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective text, January 2017

Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems? text, January 2017

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

The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
text, January 2014

A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
text, January 2014

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
text, January 2015

A practical guide to density matrix embedding theory in quantum chemistry
text, January 2016

Quantum embedding theories
text, January 2016

Stripe order in the underdoped region of the two-dimensional Hubbard model
text, January 2017

Block product density matrix embedding theory for strongly correlated spin systems
text, January 2017

Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
text, January 2017

Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
text, January 2017