Renyi entropy of the interacting Fermi liquid

Abstract

Entanglement properties, including the Renyi $\ensuremath{\alpha}$ entropies and scaling laws, are becoming increasingly important in condensed-matter physics because they can be used to determine physical properties and the ``fingerprint'' of quantum phases. In this work we use variational quantum Monte Carlo to compute the Renyi $\ensuremath{\alpha}$ entropies, their scaling laws, and the relationship between different $\ensuremath{\alpha}$ entropies for one of the most important phases in condensed matter, the interacting Fermi liquid. We also investigate the relationship between the scaling laws and the discontinuity in the momentum distribution at the Fermi surface. Contrary to recent theoretical predictions, we find that interactions increase the prefactor for the $\ensuremath{\alpha}$-entropy scaling laws for all particle interaction strengths and forms. We also show that a theory of these scaling laws for the interacting systems may be developed by extending the free theory to incorporate properties of the momentum distribution.