Optimal Real-Space Renormalization-Group Transformations with Artificial Neural Networks

TL;DR

This paper presents a method using neural networks to optimize real-space renormalization-group transformations, accurately estimating critical exponents in the 2D Ising model by minimizing divergence between distributions.

Contribution

It introduces a neural network-based optimization scheme for real-space RG transformations, improving the accuracy of critical property calculations.

Findings

Achieved a highly accurate thermal critical exponent y_t=1.0001(11).

Demonstrated effectiveness of neural network optimization in RG transformations.

Abstract

We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system. The scheme is based on minimizing the Kullback-Leibler divergence between the distribution of the system and the normalized normalizing factor of the transformation parametrized by a restricted Boltzmann machine. We compute the thermal critical exponent of the two-dimensional Ising model using the trained optimal projector and obtain a very accurate thermal critical exponent $y_t=1.0001(11)$ after the first step of the transformation.