Entanglement resolution of free Dirac fermions on a torus

TL;DR

This paper analyzes the symmetry-resolved entanglement entropy of massless and massive Dirac fermions on a torus, revealing how mass and boundary conditions influence charge distribution and negativity resolution.

Contribution

It provides the first detailed evaluation of symmetry-resolved entanglement entropy for Dirac fermions on a torus, including effects of mass and boundary conditions.

Findings

Symmetry-resolved entanglement entropy is equally distributed at leading order.

Mass and boundary conditions cause subleading corrections to charge distribution.

Fermionic negativity resolution is affected by mass at subleading order.

Abstract

Whenever a system possesses a conserved charge, the density matrix splits into eigenspaces associated to the each symmetry sector and we can access the entanglement entropy in a given subspace, known as symmetry resolved entanglement (SRE). Here, we first evaluate the SRE for massless Dirac fermions in a system at finite temperature and size, i.e. on a torus. Then we add a massive term to the Dirac action and we treat it as a perturbation of the massless theory. The charge-dependent entropies turn out to be equally distributed among all the symmetry sectors at leading order. However, we find subleading corrections which depend both on the mass and on the boundary conditions along the torus. We also study the resolution of the fermionic negativity in terms of the charge imbalance between two subsystems. We show that also for this quantity, the presence of the mass alters the equipartition among the different imbalance sectors at subleading order.