Excited state entanglement in homogeneous fermionic chains

We study the Rényi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free, translational invariant Hamiltonian. In order to analytically compute the entropy we use two technical tools. The first is used to logarithmically reduce the complexity of the problem and the second to compute the Rényi entropy of the chosen subsystem. We introduce new strategies to perform the computations, derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome. Finally we discuss the physical interpretation of our results and generalize them to compute the entanglement entropy for a fragment of a fermionic ladder.