Transition matrix Monte Carlo method for quantum systems

TL;DR

This paper introduces a novel Monte Carlo method for quantum lattice models that efficiently computes free energy and entropy across all temperatures with high precision, leveraging recent Monte Carlo techniques.

Contribution

It develops a transition matrix Monte Carlo approach for quantum systems, providing an exact relation between DOS and transition probabilities to improve accuracy.

Findings

High-precision free energy and entropy calculations across temperature ranges

Reduction of statistical errors in quantum Monte Carlo estimates

Effective integration of loop algorithm with transition matrix methods

Abstract

We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole range of temperature. The method is based on several recent findings in Monte Carlo techniques, such as the loop algorithm and the transition matrix Monte Carlo method. In particular, we derive an exact relation between the DOS and the expectation value of the transition probability for quantum systems, which turns out to be useful in reducing the statistical errors in various estimates.