Entanglement Entropy and the Fermi Surface

Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size L in d spatial dimensions is S similar to L(d-1) logL, a result that should be contrasted with the usual boundary law S similar to Ld(-1). This term depends only on the geometry of the Fermi surface and on the boundary of the region in question. I give an intuitive account of this anomalous scaling based on a low energy description of the Fermi surface as a collection of one-dimensional gapless modes. Using this picture, I predict a violation of the boundary law in a number of other strongly correlated systems.