# Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles

## TL;DR

This paper introduces symmetric minimally entangled typical thermal states (METTS) for efficient simulation of finite-temperature quantum systems, leveraging symmetries and novel collapse bases to improve convergence and reduce computational costs.

## Contribution

It presents new symmetric Fourier and Haar-random collapse bases for METTS, enabling efficient simulation of canonical and grand-canonical ensembles with reduced autocorrelations.

## Key findings

- Symmetric bases improve autocorrelation decay.
- Efficient simulation of grand-canonical ensembles.
- Enhanced convergence speeds in spin chain models.

## Abstract

Based on the density matrix renormalization group (DMRG), strongly correlated quantum many-body systems at finite temperatures can be simulated by sampling over a certain class of pure matrix product states (MPS) called minimally entangled typical thermal states (METTS). When a system features symmetries, these can be utilized to substantially reduce MPS computation costs. It is conceptually straightforward to simulate canonical ensembles using symmetric METTS. In practice, it is important to alternate between different symmetric collapse bases to decrease autocorrelations in the Markov chain of METTS. To this purpose, we introduce symmetric Fourier and Haar-random block bases that are efficiently mixing. We also show how grand-canonical ensembles can be simulated efficiently with symmetric METTS. We demonstrate these approaches for spin-1/2 XXZ chains and discuss how the choice of the collapse bases influences autocorrelations as well as the distribution of measurement values and, hence, convergence speeds.