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

Understand

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.