Neural-network quantum states at finite temperature

TL;DR

This paper introduces a neural network-based approach to compute the thermal equilibrium states of many-body quantum systems, enabling efficient finite-temperature simulations.

Contribution

It presents a novel neural network variational method to represent the density matrix at finite temperature, demonstrated on the Bose-Hubbard model.

Findings

Accurately reproduces finite-temperature states of the Bose-Hubbard model.

Shows agreement with exact diagonalization results.

Provides a scalable approach for quantum thermal states.

Abstract

We propose a method to obtain the thermal-equilibrium density matrix of a many-body quantum system using artificial neural networks. The variational function of the many-body density matrix is represented by a convolutional neural network with two input channels. We first prepare an infinite-temperature state, and the temperature is lowered by imaginary-time evolution. We apply this method to the one-dimensional Bose-Hubbard model and compare the results with those obtained by exact diagonalization.