Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics

TL;DR

This paper derives a detailed asymptotic expansion for the entanglement entropy and spectrum of noninteracting 1D fermions on a line, including finite-size corrections, based on full counting statistics.

Contribution

It provides the first comprehensive asymptotic expansion for entanglement entropy and spectrum in this system, extending previous leading-order results with explicit correction terms.

Findings

Finite-size corrections to entanglement entropy are derived.

The asymptotic expansion for Renyi entropies matches earlier results.

Entanglement spectrum is characterized in terms of single-particle occupation numbers.

Abstract

We consider the entanglement entropy for a line segment in the system of noninteracting one-dimensional fermions at zero temperature. In the limit of a large segment length L, the leading asymptotic behavior of this entropy is known to be logarithmic in L. We study finite-size corrections to this asymptotic behavior. Based on an earlier conjecture of the asymptotic expansion for full counting statistics in the same system, we derive a full asymptotic expansion for the von Neumann entropy and obtain first several corrections for the Renyi entropies. Our corrections for the Renyi entropies reproduce earlier results. We also discuss the entanglement spectrum in this problem in terms of single-particle occupation numbers.