Entanglement Entropy in Fermi Gases and Anderson's Orthogonality Catastrophe

We study the ground-state entanglement entropy of a finite subsystem of size L of an infinite system of noninteracting fermions scattered by a potential of finite range a. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove that for a one-dimensional symmetric potential the von Neumann entropy, the Renyi entropies, and the full counting statistics are robust against potential scattering, provided that L/a >> 1. The results of numerical calculations support the validity of this conclusion for a generic potential.