Renyi Entropy of the Interacting Fermi Liquid

Entanglement properties, including the Renyi $\alpha$-entropies and scaling laws, are becoming increasingly important in condensed matter physics. In this work we use variational quantum Monte Carlo to compute the Renyi $\alpha$-entropies, their scaling laws, and the relationship between different $\alpha$-entropies for one of the most important phases in condensed matter, the interacting Fermi liquid. Contrary to recent theoretical predictions, we find that interactions increase the prefactor for the $\alpha$-entropy scaling laws for all particle interaction strengths and forms.