Fixed Point Quantum Monte Carlo

TL;DR

This paper introduces a novel quantum Monte Carlo method that leverages Laplace transforms and stochastic unravellings to efficiently compute equilibrium properties of many-body quantum systems, especially when interactions are weak.

Contribution

The paper presents a new quantum Monte Carlo approach that uses Laplace representation and stochastic unravellings, improving efficiency and accuracy over existing methods.

Findings

Accurately computes equilibrium properties in quantum many-body systems.

Demonstrates improved convergence when interaction parameters are small.

Shows efficiency and accuracy through condensed matter physics case studies.

Abstract

We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is transferred to the Laplace representation where an exact equation can be derived and solved using a simulation-step that, unlike most Monte Carlo methods, is not a priori physically bounded. Moreover, the spawning events are formulated in terms of two-process stochastic unravellings of quantum master equations, a formalism that is particularly useful when working with density matrices. And last, this is equivalent to an interaction picture, where the free part is integrated exactly and the convergence rate can be greatly increased if the interaction parameter is small. We benchmark our method by applying it to two case-studies in condensed matter physics, show its accuracy and further discuss its efficiency.