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:
-
- Princeton Univ., NJ (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- 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}
}
Web of Science
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