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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: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: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
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Cited by: 17 works
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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

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