A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations

TL;DR

This paper introduces a Wang-Landau sampling method in quantum Monte Carlo simulations to efficiently compute Renyi entropies and mutual information, enabling direct estimation without thermodynamic integration.

Contribution

The authors develop and implement a Wang-Landau algorithm for QMC that estimates the density of states for calculating Renyi entropies directly, improving upon traditional importance sampling methods.

Findings

Successfully benchmarked on various 2D and 3D spin models.

Confirmed critical scaling of mutual information at finite-temperature transitions.

Demonstrated advantages and limitations of broad sampling techniques.

Abstract

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density of states for Stochastic Series Expansion QMC allowing a direct calculation of Renyi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.