Free-fermion entanglement and spheroidal functions

TL;DR

This paper explores the entanglement properties of one-dimensional free fermions, linking the problem to spheroidal functions and differential equations, with results aligning with other methods and connections to random matrix theory.

Contribution

It introduces an approach connecting free fermion entanglement to spheroidal functions, providing analytical eigenvalue spectra consistent with existing methods.

Findings

Eigenfunctions are spheroidal functions or their generalizations.

Analytical eigenvalue spectra match previous results.

Connections to random matrix theory in the continuum case.

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.