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

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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• Temperature evolution of the phonon dynamics in the Kitaev spin liquid
• Network-Initialized Monte Carlo Based on Generative Neural Networks
• Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
• Ratio Divergence Learning Using Target Energy in Restricted Boltzmann Machines: Beyond Kullback--Leibler Divergence Learning
• Learning a compass spin model with neural network quantum states
• Efficient bit encoding of neural networks for Fock states