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arXiv · 1007.4825

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

Brian Swingle
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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.

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Brian Swingle. 2010-07-27. Renyi entropy, mutual information, and fluctuation properties of Fermi liquids. https://doi.org/10.1103/physrevb.86.045109

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