Autoregressive Typical Thermal States

TL;DR

This paper introduces an autoregressive neural network framework for calculating finite-temperature properties of quantum systems, addressing numerical instabilities and demonstrating accurate results on a quantum spin chain.

Contribution

It presents a novel autoregressive approach for quantum thermal states, improving stability and accuracy over existing methods like METTS.

Findings

Autoregressive models can accurately compute thermal observables.

Numerical instabilities in METTS are mitigated with unitary evolution and thresholds.

The method shows strong agreement with exact results for the XY chain.

Abstract

A variety of generative neural networks recently adopted from machine learning have provided promising strategies for studying quantum matter. In particular, the success of autoregressive models in natural language processing has motivated their use as variational ans\"atze, with the hope that their demonstrated ability to scale will transfer to simulations of quantum many-body systems. In this paper, we introduce an autoregressive framework to calculate finite-temperature properties of a quantum system based on the imaginary-time evolution of an ensemble of pure states. We find that established approaches based on minimally entangled typical thermal states (METTS) have numerical instabilities when an autoregressive recurrent neural network is used as the variational ans\"atz. We show that these instabilities can be mitigated by evolving the initial ensemble states with a unitary operation, along with applying a threshold to curb runaway evolution of ensemble members. By comparing our algorithm to exact results for the spin 1/2 quantum XY chain, we demonstrate that autoregressive typical thermal states are capable of accurately calculating thermal observables.