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

Abstract: We study bipartite entanglement entropies in the ground and excited states of model fermion systems, where a staggered potential, $\mu_s$, induces a gap in the spectrum. Ground state entanglement entropies satisfy the area law', and thearea-law' coefficient is found to diverge as a logarithm of the staggered potential, when the system has an extended Fermi surface at $\mu_s=0$. On the square-lattice, we show that the coefficient of the logarithmic divergence depends on the fermi surface geometry and its orientation with respect to the real-space interface between subsystems and is related to the Widom conjecture as enunciated by Gioev and Klich (Phys. Rev. Lett. 96, 100503 (2006)). For point Fermi surfaces in two-dimension, the area-law' coefficient stays finite as $\mu_s\to 0$. The von Neumann entanglement entropy associated with the excited states follows avolume law' and allows us to calculate an entropy density function s_{V}(e), which is substantially different from the thermodynamic entropy density function $s_{T}(e)$, when the lattice is bipartitioned into two equal subsystems but approaches the thermodynamic entropy density as the fraction of sites in the larger subsystem, that is integrated out, approaches unity.