Improving entanglement and thermodynamic Renyi entropy measurements in quantum Monte Carlo

We present a method for improving measurements of the entanglement Renyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation Renyi entropies. Exploiting the capability of building improved estimators for the latter makes it possible to obtain very good estimates for entanglement Renyi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated, providing access to the thermodynamic Renyi entropies with high accuracy. We also explore a recently proposed method for the reconstruction of the entanglement spectrum from entanglement Renyi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal Renyi entropies.