Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature

TL;DR

This paper presents an efficient algorithm for approximating the partition functions of certain quantum spin systems at low temperatures, leveraging classical perturbation techniques and advanced algorithmic frameworks.

Contribution

It introduces a novel approximation algorithm for quantum partition functions at low temperatures, combining contour representations with modern algorithmic methods.

Findings

Algorithm efficiently approximates quantum partition functions.

Applicable to stable quantum perturbations of classical systems.

Advances computational methods for quantum statistical mechanics.

Abstract

We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on combining the contour representation of quantum spin systems of this type due to Borgs, Koteck\'y, and Ueltschi with the algorithmic framework developed by Helmuth, Perkins, and Regts, and Borgs et al.