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We study bipartite entanglement entropies in the ground and excited states ofmodel fermion systems, where a staggered potential, $\mu_s$, induces a gap inthe spectrum. Ground state entanglement entropies satisfy the `area law', andthe `area-law' coefficient is found to diverge as a logarithm of the staggeredpotential, when the system has an extended Fermi surface at $\mu_s=0$. On thesquare-lattice, we show that the coefficient of the logarithmic divergencedepends on the fermi surface geometry and its orientation with respect to thereal-space interface between subsystems and is related to the Widom conjectureas enunciated by Gioev and Klich (Phys. Rev. Lett. 96, 100503 (2006)). Forpoint Fermi surfaces in two-dimension, the `area-law' coefficient stays finiteas $\mu_s\to 0$. The von Neumann entanglement entropy associated with theexcited states follows a `volume law' and allows us to calculate an entropydensity function s_{V}(e), which is substantially different from thethermodynamic entropy density function $s_{T}(e)$, when the lattice isbipartitioned into two equal subsystems but approaches the thermodynamicentropy density as the fraction of sites in the larger subsystem, that isintegrated out, approaches unity.

physical review. e, statistical, nonlinear and soft matter physics

Entanglement in ground and excited states of gapped fermion systems and  their relationship with fermi surface and thermodynamic equilibrium  properties