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Title: Self-learning Monte Carlo method and cumulative update in fermion systems

Abstract

In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.

Authors:
 [1];  [1];  [1];  [2];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
  2. Chinese Academy of Sciences, Beijing (China). Institute of Physics
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1424931
Alternate Identifier(s):
OSTI ID: 1361929
Grant/Contract Number:  
SC0010526; SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 24; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Magnetism; Monte Carlo methods; Numerical techniques; Quantum Monte Carlo; statistical physics

Citation Formats

Liu, Junwei, Shen, Huitao, Qi, Yang, Meng, Zi Yang, and Fu, Liang. Self-learning Monte Carlo method and cumulative update in fermion systems. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.95.241104.
Liu, Junwei, Shen, Huitao, Qi, Yang, Meng, Zi Yang, & Fu, Liang. Self-learning Monte Carlo method and cumulative update in fermion systems. United States. doi:10.1103/PhysRevB.95.241104.
Liu, Junwei, Shen, Huitao, Qi, Yang, Meng, Zi Yang, and Fu, Liang. Wed . "Self-learning Monte Carlo method and cumulative update in fermion systems". United States. doi:10.1103/PhysRevB.95.241104. https://www.osti.gov/servlets/purl/1424931.
@article{osti_1424931,
title = {Self-learning Monte Carlo method and cumulative update in fermion systems},
author = {Liu, Junwei and Shen, Huitao and Qi, Yang and Meng, Zi Yang and Fu, Liang},
abstractNote = {In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.},
doi = {10.1103/PhysRevB.95.241104},
journal = {Physical Review B},
number = 24,
volume = 95,
place = {United States},
year = {2017},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 14 works
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Figures / Tables:

FIG. 1 FIG. 1: The trained parameters Jn for the effective model in Eq. (8) for L = 4.

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.