Rényi entanglement entropy in fermionic chains

Abstract

In this paper we discuss the asymptotic behavior of the entanglement entropy for a fragment of a fermionic chain in an excited state. We first study the case in which the subsystem consists of a single interval. We review the analytical tools that make the computation feasible, derived from the asymptotics of the determinant of Toeplitz matrices, we also compare with the numerical results and give a physical interpretation of them. Next we move to the case in which the fragment is made of several disjoint intervals. We compute numerically the entropy and, based on these results, we establish a conjecture on the determinant of a submatrix of a Toeplitz matrix that leads to a general expression for the entropy in the multi-interval case. We check that our results agree with those derived from conformal field theory when the latter are available.