Off-Diagonal Expansion Quantum Monte Carlo

TL;DR

The paper introduces a Monte Carlo algorithm that effectively simulates quantum and classical systems at equilibrium by bridging the gap between existing thermal simulation methods, using a novel partition function decomposition.

Contribution

A new Monte Carlo method based on a series expansion of the quantum partition function, unifying quantum and classical thermal simulations.

Findings

Effective simulation of quantum many-body systems with mixed behaviors

Unification of quantum and classical parallel tempering techniques

Demonstrated advantages over existing simulation schemes

Abstract

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from `fully-quantum' to `fully-classical', in contrast to many existing methods. We demonstrate the advantages of the technique by comparing it against existing schemes. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.