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

Abstract

In this work, we investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U/t=2,4,6. These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U/t=2.

Authors:
 [1];  [2];  [3];  [3];  [2]
  1. Princeton Univ., NJ (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. California Institute of Technology (CalTech), Pasadena, CA (United States)
  3. College of William and Mary, Williamsburg, VA (United States)
Publication Date:
Research Org.:
Princeton Univ., NJ (United States); College of William and Mary, Williamsburg, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1535837
Alternate Identifier(s):
OSTI ID: 1338105
Grant/Contract Number:  
SC0008624; SC0008627; SC0010530
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 4; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Cluster methods; finite-size scaling; Hubbard model; quantum Monte Carlo

Citation Formats

Zheng, Bo-Xiao, Kretchmer, Joshua S., Shi, Hao, Zhang, Shiwei, and Chan, Garnet Kin-Lic. Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver. United States: N. p., 2017. Web. doi:10.1103/physrevb.95.045103.
Zheng, Bo-Xiao, Kretchmer, Joshua S., Shi, Hao, Zhang, Shiwei, & Chan, Garnet Kin-Lic. Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver. United States. https://doi.org/10.1103/physrevb.95.045103
Zheng, Bo-Xiao, Kretchmer, Joshua S., Shi, Hao, Zhang, Shiwei, and Chan, Garnet Kin-Lic. 2017. "Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver". United States. https://doi.org/10.1103/physrevb.95.045103. https://www.osti.gov/servlets/purl/1535837.
@article{osti_1535837,
title = {Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver},
author = {Zheng, Bo-Xiao and Kretchmer, Joshua S. and Shi, Hao and Zhang, Shiwei and Chan, Garnet Kin-Lic},
abstractNote = {In this work, we investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U/t=2,4,6. These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U/t=2.},
doi = {10.1103/physrevb.95.045103},
url = {https://www.osti.gov/biblio/1535837}, journal = {Physical Review. B},
issn = {2469-9950},
number = 4,
volume = 95,
place = {United States},
year = {Tue Jan 03 00:00:00 EST 2017},
month = {Tue Jan 03 00:00:00 EST 2017}
}

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Cited by: 27 works
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Works referenced in this record:

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Works referencing / citing this record:

Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
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A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics
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Incremental embedding: A density matrix embedding scheme for molecules
journal, November 2018


An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas
journal, May 2019


Energy-weighted density matrix embedding of open correlated chemical fragments
journal, July 2019


Projected density matrix embedding theory with applications to the two-dimensional Hubbard model
journal, August 2019


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


Rigorous wave function embedding with dynamical fluctuations
journal, December 2018


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


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


Periodic Electronic Structure Calculations With Density Matrix Embedding Theory
preprint, January 2019