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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: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. doi: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 = {2017},
month = {6}
}

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

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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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Works referenced in this record:

On the product of semi-groups of operators
journal, April 1959


Considerations on Double Exchange
journal, October 1955


Monte Carlo Method for Magnetic Impurities in Metals
journal, June 1986


Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices
journal, June 2015


Sign-Problem-Free Quantum Monte Carlo of the Onset of Antiferromagnetism in Metals
journal, December 2012


Self-learning Monte Carlo method
journal, January 2017


A Theory of Metallic Ferro- and Antiferromagnetism on Zener's Model
journal, July 1956

  • Kasuya, Tadao
  • Progress of Theoretical Physics, Vol. 16, Issue 1
  • DOI: 10.1143/PTP.16.45

A Monte Carlo Method for Fermion Systems Coupled with Classical Degrees of Freedom
journal, December 1999

  • Motome, Yukitoshi; Furukawa, Nobuo
  • Journal of the Physical Society of Japan, Vol. 68, Issue 12
  • DOI: 10.1143/JPSJ.68.3853

Calculation of Partition Functions
journal, July 1959


Enhancement of Superconductivity near a Nematic Quantum Critical Point
journal, March 2015


Numerical study of the two-dimensional Hubbard model
journal, July 1989


Topological phase transitions with SO(4) symmetry in (2+1)D interacting Dirac fermions
journal, February 2017


Hybrid Monte Carlo algorithm for the double exchange model
journal, March 2001


Collective Monte Carlo Updating for Spin Systems
journal, January 1989


Effects of Double Exchange in Magnetic Crystals
journal, April 1960


Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons
journal, October 1954


Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985


Competing Orders in a Nearly Antiferromagnetic Metal
journal, August 2016


Nonuniversal critical dynamics in Monte Carlo simulations
journal, January 1987


Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981


Magnetic Properties of Cu-Mn Alloys
journal, June 1957


Equation of State Calculations by Fast Computing Machines
journal, June 1953

  • Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.
  • The Journal of Chemical Physics, Vol. 21, Issue 6
  • DOI: 10.1063/1.1699114

Computational Studies of Quantum Spin Systems
conference, January 2010

  • Sandvik, Anders W.; Avella, Adolfo; Mancini, Ferdinando
  • LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XIV: Fourteenth Training Course in the Physics of Strongly Correlated Systems, AIP Conference Proceedings
  • DOI: 10.1063/1.3518900

A travelling cluster approximation for lattice fermions strongly coupled to classical degrees of freedom
journal, April 2006


Monte Carlo sampling methods using Markov chains and their applications
journal, April 1970


The truncated polynomial expansion Monte Carlo method for fermion systems coupled to classical fields: a model independent implementation
journal, May 2005


Frustration-Induced Insulating Chiral Spin State in Itinerant Triangular-Lattice Magnets
journal, November 2010


Ising Nematic Quantum Critical Point in a Metal: A Monte Carlo Study
journal, August 2016


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