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:
-
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
- 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. https://doi.org/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. https://doi.org/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 = {Wed Jun 07 00:00:00 EDT 2017},
month = {Wed Jun 07 00:00:00 EDT 2017}
}
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Cited by: 61 works
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Figures / Tables:
FIG. 1: The trained parameters Jn for the effective model in Eq. (8) for L = 4.
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