Matrix product state techniques for two-dimensional systems at finite temperature

TL;DR

This paper extends matrix product state techniques to two-dimensional systems at finite temperature, combining purification, linked-cluster expansions, and METTS algorithms to study quantum lattice models.

Contribution

It introduces a comprehensive approach for finite-temperature simulations of 2D quantum systems using MPS techniques, including new methods for critical temperature extraction.

Findings

Excellent agreement with existing methods for the triangular Heisenberg antiferromagnet.

Successful extraction of critical temperatures using METTS-based approach.

Comparison shows Suzuki-Trotter with swap gates is most accurate for imaginary-time evolution.

Abstract

The density matrix renormalization group is one of the most powerful numerical methods for computing ground-state properties of two-dimensional (2D) quantum lattice systems. Here we show its finite-temperature extensions are also viable for 2D, using the following strategy: At high temperatures, we combine density-matrix purification and numerical linked-cluster expansions to extract static observables directly in the thermodynamic limit. At low temperatures inaccessible to purification, we use the minimally entangled typical thermal state (METTS) algorithm on cylinders. We consider the triangular Heisenberg antiferromagnet as a first application, finding excellent agreement with other state of the art methods. In addition, we present a METTS-based approach that successfully extracts critical temperatures, and apply it to a frustrated lattice model. On a technical level, we compare two different schemes for performing imaginary-time evolution of 2D clusters, finding that a Suzuki-Trotter decomposition with swap gates is currently the most accurate and efficient.