Calculating Thermodynamics Properties of Quantum Systems by a non-Markovian Monte Carlo Procedure

TL;DR

This paper introduces a history-dependent Monte Carlo method inspired by Wang-Landau sampling and metadynamics for efficiently calculating thermodynamic properties of quantum systems, applicable to various Hamiltonians.

Contribution

It presents a novel non-Markovian Monte Carlo scheme embedded in a path integral framework, demonstrating improved accuracy and efficiency over existing methods.

Findings

Accurately computes free energy, critical temperature, and specific heat.

Shows superior performance compared to Wang-Landau method.

Validates approach on the two-dimensional quantum Ising model.

Abstract

We present a history-dependent Monte Carlo scheme for the efficient calculation of the free-energy of quantum systems, inspired by the Wang-Landau sampling and metadynamics method. When embedded in a path integral formulation, it is of general applicability to a large variety of Hamiltonians. In the two-dimensional quantum Ising model, chosen here for illustration, the accuracy of free energy, critical temperature, and specific heat is demonstrated as a function of simulation time, and successfully compared with the best available approaches, particularly the Wang-Landau method over two different Monte Carlo procedures.