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

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.

9 pages, 3 big figures

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• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
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