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

TL;DR

This paper demonstrates that convolutional restricted Boltzmann machines can efficiently accelerate Monte Carlo simulations for complex many-body systems like the Ising and Kitaev models by leveraging translation invariance.

Contribution

It introduces the use of CRBM to reduce parameters and enable training on smaller lattices for larger system simulations in condensed matter physics.

Findings

CRBM reduces the number of parameters needed for training.

CRBM trained on small lattices can be applied to larger lattices.

Efficiently applied to Ising and Kitaev models in two dimensions.

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.