Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy

TL;DR

This paper extends the Wang-Landau algorithm to quantum systems, enabling efficient computation of free energy and entropy, especially near phase transitions, by overcoming tunneling issues present in classical methods.

Contribution

The authors develop a quantum generalization of the Wang-Landau algorithm that evaluates high temperature series coefficients to improve sampling near phase transitions.

Findings

Reduces tunneling problems at quantum phase transitions

Allows direct calculation of free energy and entropy in quantum systems

Efficiently handles first order phase transitions

Abstract

We present a generalization of the classical Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] to quantum systems. The algorithm proceeds by stochastically evaluating the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order. Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct calculation of the free energy and entropy.