Entanglement entropies in free fermion gases for arbitrary dimension

TL;DR

This paper analyzes how entanglement entropy scales in free fermion gases across different dimensions, revealing a universal asymptotic growth pattern involving N and a logarithmic correction.

Contribution

It provides an analytical derivation of the entanglement entropy growth in arbitrary dimensions using the Widom conjecture, extending understanding beyond specific cases.

Findings

Entanglement entropies grow as N^(1-1/d) ln N for large N.

The prefactor is analytically computed for both periodic and open boundaries.

Numerical calculations confirm the asymptotic behavior.

Abstract

We study the entanglement entropy of connected bipartitions in free fermion gases of N particles in arbitrary dimension d. We show that the von Neumann and Renyi entanglement entropies grow asymptotically as N^(1-1/d) ln N, with a prefactor that is analytically computed using the Widom conjecture both for periodic and open boundary conditions. The logarithmic correction to the power-law behavior is related to the area-law violation in lattice free fermions. These asymptotic large-N behaviors are checked against exact numerical calculations for N-particle systems.