Entanglement Entropy and the Fermi Surface

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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 Lᵈ⁻¹ L, a result that should be contrasted with the usual boundary law S 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.