Convolutional restricted Boltzmann machine aided Monte Carlo: An application to Ising and Kitaev models

Daniel Alcalde Puente and Ilya M. Eremin
Phys. Rev. B 102, 195148 – Published 30 November 2020

Abstract

Machine learning is becoming widely used in analyzing the thermodynamics of many-body condensed matter systems. Restricted Boltzmann machine (RBM) aided Monte Carlo simulations have sparked interest recently, as they manage to speed up classical Monte Carlo simulations. Here we employ the convolutional restricted Boltzmann machine (CRBM) method and show that its use helps to reduce the number of parameters to be learned drastically by taking advantage of translation invariance. Furthermore, we show that it is possible to train the CRBM at smaller lattice sizes, and apply it to larger lattice sizes. To demonstrate the efficiency of CRBM we apply it to the paradigmatic Ising and Kitaev models in two dimensions.

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  • Received 20 April 2020
  • Revised 1 October 2020
  • Accepted 19 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.195148

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel Alcalde Puente and Ilya M. Eremin

  • Institut für Theoretische Physik III, Ruhr-Universität Bochum, D-44780 Bochum, Germany

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Issue

Vol. 102, Iss. 19 — 15 November 2020

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