skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Self-learning Monte Carlo method: Continuous-time algorithm

Abstract

The recently introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of a continuous-time Monte Carlo method with an auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. Furthermore, by using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.

Authors:
 [1];  [2];  [2];  [3];  [2]
  1. Japan Atomic Energy Agency, Chiba (Japan); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Hong Kong Univ. of Science and Technology, Hong Kong (China)
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:
1505622
Alternate Identifier(s):
OSTI ID: 1396308
Grant/Contract Number:  
SC0010526
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 16; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Nagai, Yuki, Shen, Huitao, Qi, Yang, Liu, Junwei, and Fu, Liang. Self-learning Monte Carlo method: Continuous-time algorithm. United States: N. p., 2017. Web. doi:10.1103/physrevb.96.161102.
Nagai, Yuki, Shen, Huitao, Qi, Yang, Liu, Junwei, & Fu, Liang. Self-learning Monte Carlo method: Continuous-time algorithm. United States. doi:https://doi.org/10.1103/physrevb.96.161102
Nagai, Yuki, Shen, Huitao, Qi, Yang, Liu, Junwei, and Fu, Liang. Tue . "Self-learning Monte Carlo method: Continuous-time algorithm". United States. doi:https://doi.org/10.1103/physrevb.96.161102. https://www.osti.gov/servlets/purl/1505622.
@article{osti_1505622,
title = {Self-learning Monte Carlo method: Continuous-time algorithm},
author = {Nagai, Yuki and Shen, Huitao and Qi, Yang and Liu, Junwei and Fu, Liang},
abstractNote = {The recently introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of a continuous-time Monte Carlo method with an auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. Furthermore, by using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.},
doi = {10.1103/physrevb.96.161102},
journal = {Physical Review B},
number = 16,
volume = 96,
place = {United States},
year = {2017},
month = {10}
}

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

Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Schematic figure for the Markov chains in the original and self-learning continuous-time Monte Carlo methods to obtain an uncorrelated configuration. $n$ denotes the average expansion order that determines the size of the matrix Nσ({si, τi}), and further determines the complexity of the simulation. See the last section ofmore » this Rapid Communication for a detailed discussion.« less

Save / Share:

Works referenced in this record:

Momentum-selective metal-insulator transition in the two-dimensional Hubbard model: An 8-site dynamical cluster approximation study
journal, July 2009


Quantum Entanglement in Neural Network States
journal, May 2017


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


Self-learning Monte Carlo method
journal, January 2017


Accelerated Monte Carlo simulations with restricted Boltzmann machines
journal, January 2017


Low-temperature density matrix renormalization group using regulated polynomial expansion
journal, September 2008


Superconductivity from Emerging Magnetic Moments
journal, December 2015


Numerical evaluation of Green's functions based on the Chebyshev expansion
journal, October 2014


Localized Magnetic States in Metals
journal, October 1961


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


Efficient Numerical Approach to Inhomogeneous Superconductivity: The Chebyshev-Bogoliubov–de Gennes Method
journal, October 2010


Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011

  • Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
  • Reviews of Modern Physics, Vol. 83, Issue 2
  • DOI: 10.1103/RevModPhys.83.349

Efficient Numerical Self-Consistent Mean-Field Approach for Fermionic Many-Body Systems by Polynomial Expansion on Spectral Density
journal, February 2012

  • Nagai, Yuki; Ota, Yukihiro; Machida, Masahiko
  • Journal of the Physical Society of Japan, Vol. 81, Issue 2
  • DOI: 10.1143/JPSJ.81.024710

Self-learning quantum Monte Carlo method in interacting fermion systems
journal, July 2017


Recommender engine for continuous-time quantum Monte Carlo methods
journal, March 2017


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


Critical temperature enhancement of topological superconductors: A dynamical mean-field study
journal, June 2016


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


Continuous-time auxiliary-field Monte Carlo for quantum impurity models
journal, May 2008


Electronic orders in multiorbital Hubbard models with lifted orbital degeneracy
journal, April 2016


Continuous-time quantum Monte Carlo method for fermions
journal, July 2005


Self-learning Monte Carlo method and cumulative update in fermion systems
journal, June 2017


Quantum Loop Topography for Machine Learning
journal, May 2017


Detection of Phase Transition via Convolutional Neural Networks
journal, June 2017

  • Tanaka, Akinori; Tomiya, Akio
  • Journal of the Physical Society of Japan, Vol. 86, Issue 6
  • DOI: 10.7566/JPSJ.86.063001

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination
journal, June 2017


Learning phase transitions by confusion
journal, February 2017

  • van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D.
  • Nature Physics, Vol. 13, Issue 5
  • DOI: 10.1038/nphys4037

Solving the quantum many-body problem with artificial neural networks
journal, February 2017


Machine learning phases of matter
journal, February 2017

  • Carrasquilla, Juan; Melko, Roger G.
  • Nature Physics, Vol. 13, Issue 5
  • DOI: 10.1038/nphys4035

Submatrix updates for the continuous-time auxiliary-field algorithm
journal, February 2011


Continuous-Time Solver for Quantum Impurity Models
journal, August 2006


Chebyshev matrix product state impurity solver for dynamical mean-field theory
journal, September 2014


New tool in the box
journal, February 2017


    Works referencing / citing this record:

    Accelerating small-angle scattering experiments on anisotropic samples using kernel density estimation
    journal, February 2019


    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

    Revealing fermionic quantum criticality from new Monte Carlo techniques
    journal, August 2019

    • Xu, Xiao Yan; Hong Liu, Zi; Pan, Gaopei
    • Journal of Physics: Condensed Matter, Vol. 31, Issue 46
    • DOI: 10.1088/1361-648x/ab3295

    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


    Real-space mapping of topological invariants using artificial neural networks
    journal, March 2018


    Self-learning Monte Carlo with deep neural networks
    journal, May 2018


    Symmetry-enforced self-learning Monte Carlo method applied to the Holstein model
    journal, July 2018


    Itinerant quantum critical point with frustration and a non-Fermi liquid
    journal, July 2018


    Deep learning topological invariants of band insulators
    journal, August 2018


    Elective-momentum ultrasize quantum Monte Carlo method
    journal, February 2019


    Flow-based generative models for Markov chain Monte Carlo in lattice field theory
    journal, August 2019


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


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


    Machine Learning Topological Invariants with Neural Networks
    journal, February 2018


    Discriminative Cooperative Networks for Detecting Phase Transitions
    journal, April 2018


    Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
    journal, February 2019


    Machine learning and the physical sciences
    journal, December 2019


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