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Self-learning Monte Carlo method and cumulative update in fermion systems

Journal Article · · Physical Review B
 [1];  [2];  [2];  [3];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics; Massachusetts Institute of Technology
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
  3. Chinese Academy of Sciences, Beijing (China). Institute of Physics
+ Show Author Affiliations
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.
Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
Grant/Contract Number:
SC0001299; SC0010526
OSTI ID:
1424931
Alternate ID(s):
OSTI ID: 1361929
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 24 Vol. 95; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Self-learning Monte Carlo method: Continuous-time algorithm journal October 2017
Principal component analysis for fermionic critical points journal November 2017
Restricted Boltzmann machine learning for solving strongly correlated quantum systems journal November 2017
Approximating quantum many-body wave functions using artificial neural networks journal January 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
Self-organizing maps as a method for detecting phase transitions and phase identification journal January 2019
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
Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines journal October 2019
Exploring cluster Monte Carlo updates with Boltzmann machines 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
Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system journal February 2019
Machine learning of phase transitions in the percolation and X Y models journal March 2019
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
Non-Fermi Liquid at ( 2 + 1 ) D Ferromagnetic Quantum Critical Point journal September 2017
Machine learning and the physical sciences journal December 2019
All-optical neural network with nonlinear activation functions journal January 2019
Approximating quantum many-body wave-functions using artificial neural networks text January 2017
Self-Learning Monte Carlo Method: Continuous-Time Algorithm text January 2017
Itinerant quantum critical point with frustration and non-Fermi-liquid text January 2017
Machine Learning Topological Invariants with Neural Networks text January 2017
Self-learning Monte Carlo with Deep Neural Networks text January 2018
Machine learning of phase transitions in the percolation and XY models text January 2018
Deep Learning Topological Invariants of Band Insulators text January 2018
Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system text January 2018
Self-organizing maps as a method for detecting phase transitions and phase identification text January 2018
All Optical Neural Network with Nonlinear Activation Functions text January 2019
Flow-based generative models for Markov chain Monte Carlo in lattice field theory text January 2019
Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines text January 2019

Figures / Tables (4)

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Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Magnetism
Monte Carlo methods
Numerical techniques
Quantum Monte Carlo
statistical physics