Momentum-space entanglement for interacting fermions at finite density

TL;DR

This paper studies how individual modes in finite-density fermionic systems become entangled, especially near the Fermi surface, revealing divergences and mode correlations using perturbative calculations.

Contribution

It provides a perturbative analysis of mode entanglement in finite-density fermions, highlighting divergences near the Fermi surface and the behavior of mutual information between modes.

Findings

Entanglement entropy diverges logarithmically near the Fermi surface.

Mutual information peaks between modes just above and below the Fermi momentum.

Entanglement properties are robust under cutoff of modes away from the Fermi surface.

Abstract

We investigate the entanglement between individual field theory modes in finite-density systems of interacting relativistic and non-relativistic fermions in one spatial dimension. We calculate the entanglement entropy for a single field theory mode and the mutual information between any two modes. The calculation is perturbative in the four-fermion (two-body) coupling, with the leading contribution at order lambda^2 log(lambda^2). At this leading order, the perturbative expression for the entanglement entropy of a mode diverges logarithmically as the momentum of the mode approaches the Fermi surface from above or below. The mutual information between modes is largest for pairs of modes just above and below the Fermi momentum. The entanglement properties of modes near the Fermi surface are qualitatively the same if the field theory is cut off to eliminate modes away from the Fermi surface.