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Title: Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble

Abstract

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe thatmore » our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.« less

Authors:
ORCiD logo; ORCiD logo; ; ORCiD logo
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1724247
Grant/Contract Number:  
ERKCK29
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Name: Journal of Chemical Physics Journal Volume: 153 Journal Issue: 20; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Shen, Tong, Liu, Yuan, Yu, Yang, and Rubenstein, Brenda M. Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble. United States: N. p., 2020. Web. doi:10.1063/5.0026606.
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Shen, Tong, Liu, Yuan, Yu, Yang, & Rubenstein, Brenda M. Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble. United States. https://doi.org/10.1063/5.0026606
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Shen, Tong, Liu, Yuan, Yu, Yang, and Rubenstein, Brenda M. Wed . "Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble". United States. https://doi.org/10.1063/5.0026606.
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@article{osti_1724247,
title = {Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble},
author = {Shen, Tong and Liu, Yuan and Yu, Yang and Rubenstein, Brenda M.},
abstractNote = {Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.},
doi = {10.1063/5.0026606},
journal = {Journal of Chemical Physics},
number = 20,
volume = 153,
place = {United States},
year = {Wed Nov 25 00:00:00 EST 2020},
month = {Wed Nov 25 00:00:00 EST 2020}
}
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