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

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