Solving frustrated quantum many-particle models with convolutional neural networks

TL;DR

This paper introduces a novel convolutional neural network approach to solve highly frustrated quantum many-particle models, achieving better energy estimates than previous methods and opening new avenues for machine learning in quantum physics.

Contribution

The paper presents the first successful application of CNNs to solve the frustrated spin-1/2 J$_1$-J$_2$ antiferromagnetic Heisenberg model on square lattices.

Findings

CNN achieves lower energy per site than previous string-bond-state methods.

First demonstration of CNN solving a highly frustrated quantum model.

Establishes CNN as a promising tool for complex quantum many-particle problems.

Abstract

Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this work, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, of solving the highly frustrated spin-1/2 J$_1$-J$_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.