  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.
