Free-fermion entanglement and spheroidal functions

Abstract

We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle eigenfunctions of the entanglement Hamiltonian are then seen to be spheroidal functions or generalizations of them. The analytical results for the eigenvalue spectrum agree with those obtained by other methods. In the continuum case, there are close connections to random matrix theory.