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Title: Self-learning quantum Monte Carlo method in interacting fermion systems

Abstract

We present the self-learning Monte Carlo method is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we extend it to an interacting fermion quantum system in the framework of the widely used determinant quantum Monte Carlo. This method can generally reduce the computational complexity and moreover can greatly suppress the autocorrelation time near a critical point. This enables us to simulate an interacting fermion system on a $100 × 100$ lattice even at the critical point and obtain critical exponents with high precision.

Authors:
 [1];  [2];  [2];  [2];  [1]
+ Show Author Affiliations
  1. Chinese Academy of Sciences, Beijing (China). Beijing National Laboratory for Condensed Matter Physics and Institute of Physics; University of Chinese Academy of Sciences, Beijing (China). School of Physical Sciences
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department 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:
1424921
Alternate Identifier(s):
OSTI ID: 1371802
Grant/Contract Number:  
SC0010526
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 4; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Electron-correlation calculations; Many-body techniques; Monte Carlo methods

Citation Formats

Xu, Xiao Yan, Qi, Yang, Liu, Junwei, Fu, Liang, and Meng, Zi Yang. Self-learning quantum Monte Carlo method in interacting fermion systems. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.041119.
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Xu, Xiao Yan, Qi, Yang, Liu, Junwei, Fu, Liang, & Meng, Zi Yang. Self-learning quantum Monte Carlo method in interacting fermion systems. United States. https://doi.org/10.1103/PhysRevB.96.041119
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Xu, Xiao Yan, Qi, Yang, Liu, Junwei, Fu, Liang, and Meng, Zi Yang. Tue . "Self-learning quantum Monte Carlo method in interacting fermion systems". United States. https://doi.org/10.1103/PhysRevB.96.041119. https://www.osti.gov/servlets/purl/1424921.
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@article{osti_1424921,
title = {Self-learning quantum Monte Carlo method in interacting fermion systems},
author = {Xu, Xiao Yan and Qi, Yang and Liu, Junwei and Fu, Liang and Meng, Zi Yang},
abstractNote = {We present the self-learning Monte Carlo method is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we extend it to an interacting fermion quantum system in the framework of the widely used determinant quantum Monte Carlo. This method can generally reduce the computational complexity and moreover can greatly suppress the autocorrelation time near a critical point. This enables us to simulate an interacting fermion system on a $100 × 100$ lattice even at the critical point and obtain critical exponents with high precision.},
doi = {10.1103/PhysRevB.96.041119},
journal = {Physical Review B},
number = 4,
volume = 96,
place = {United States},
year = {Tue Jul 18 00:00:00 EDT 2017},
month = {Tue Jul 18 00:00:00 EDT 2017}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevB.96.041119
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Cited by: 52 works
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Figures / Tables:

FIG. 1 FIG. 1: (a) Schematic phase diagram of the transverse-field Ising model coupled to Fermi surface. As a function of the transverse field, the system (both fermions and Ising spins) goes through a transition from ferromagnetic (FM) metal to paramagnetic (PM) metal. The black dot is the finite-temperature critical point [Tmore » = 1,hc = 2.774(1)] where we systematically demonstrate the superior performance of SLDQMC over DQMC. (b) Autocorrelation function C($τ$ ) for L = 16 system at the critical point in panel (a), for local update with DQMC, where the autocorrelation time is very long (larger than 600 sweeps). The autocorrelation function is defined as C($τ$ ) = (〈M(0)M($τ$ )〉 − 〈M〉2)/(〈M2〉 − 〈M〉2) with M($τ$ ) being the total magnetization of Ising spins for the $τ$th sweep.« less
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    Works referencing / citing this record:

    Itinerant quantum critical point with fermion pockets and hotspots
    journal, August 2019

    • Liu, Zi Hong; Pan, Gaopei; Xu, Xiao Yan
    • Proceedings of the National Academy of Sciences, Vol. 116, Issue 34
    • DOI: 10.1073/pnas.1901751116

    Accelerating lattice quantum Monte Carlo simulations using artificial neural networks: Application to the Holstein model
    journal, July 2019

    Restricted Boltzmann machine learning for solving strongly correlated quantum systems
    journal, November 2017

    Smallest neural network to learn the Ising criticality
    journal, August 2018

    Policy-guided Monte Carlo: Reinforcement-learning Markov chain dynamics
    journal, December 2018

    Discriminative Cooperative Networks for Detecting Phase Transitions
    journal, April 2018

    Status and future perspectives for lattice gauge theory calculations to the exascale and beyond
    journal, November 2019

    • Joó, Bálint; Jung, Chulwoo; Christ, Norman H.
    • The European Physical Journal A, Vol. 55, Issue 11
    • DOI: 10.1140/epja/i2019-12919-7

    Self-Learning Monte Carlo Method: Continuous-Time Algorithm
    text, January 2017

    Itinerant quantum critical point with frustration and non-Fermi-liquid
    text, January 2017

    Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
    text, January 2017

    Machine Learning Topological Invariants with Neural Networks
    text, January 2017

    Self-learning Monte Carlo with Deep Neural Networks
    text, January 2018

    Deep Learning Topological Invariants of Band Insulators
    text, January 2018

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