Renyi entropy, mutual information, and fluctuation properties of Fermi liquids

TL;DR

This paper calculates the leading Renyi entropy contribution for Fermi liquids, revealing universal boundary law violations, and explores their mutual information and number fluctuations to characterize low-energy quantum information.

Contribution

It provides the first comprehensive calculation of Renyi entropy, mutual information, and number fluctuations in Fermi liquids, including universal boundary law violations and crossover behaviors.

Findings

Universal boundary law violating term in Renyi entropy

Universal crossover function between zero temperature and thermal entropy

Quantitative evaluation of quantum mutual information and number fluctuations

Abstract

I compute the leading contribution to the ground state Renyi entropy $S_{\alpha}$ for a region of linear size $L$ in a Fermi liquid. The result contains a universal boundary law violating term simply related the more familiar entanglement entropy. I also obtain a universal crossover function that smoothly interpolates between the zero temperature result and the ordinary thermal Renyi entropy of a Fermi liquid. Formulas for the entanglement entropy of more complicated regions, including non-convex and disconnected regions, are obtained from the conformal field theory formulation of Fermi surface dynamics. These results permit an evaluation of the quantum mutual information between different regions in a Fermi liquid. I also study the number fluctuations in a Fermi liquid. Taken together, these results give a reasonably complete characterization of the low energy quantum information content of Fermi liquids.