Matrix product state approach for a quantum system at finite temperatures using random phases and Trotter gates

TL;DR

This paper introduces an improved matrix product state method combining random phases and Trotter gates to efficiently simulate finite-temperature quantum many-body systems, overcoming limitations of previous approaches.

Contribution

It extends the random phase product state approach with Trotter gates, enhancing sampling efficiency and accuracy for finite-temperature quantum simulations.

Findings

Method achieves results consistent with the purification approach.

Successfully simulates frustrated spin systems where other methods fail.

Significantly improves sampling efficiency over original RPPS.

Abstract

We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the random phase product state (RPPS) approach introduced recently [T. Iitaka, arXiv:2006.14459]. We show that the original RPPS approach often gives unphysical values for thermodynamic quantities even in the Heisenberg chain. We find that by adding the operation of Trotter gates to the RPPS, the sampling efficiency of the approach significantly increases and its results are consistent with those of the purification approach. We also apply our method to a frustrated spin 1/2 system to exemplify that it can simulate a system in which the purification approach fails.