Universal signatures of Dirac fermions in entanglement and charge fluctuations

TL;DR

This paper demonstrates that entanglement entropy and charge fluctuations in models with massless Dirac fermions exhibit universal behavior under flux insertion, confirmed through analytical derivations and numerical checks across various models.

Contribution

It provides the first analytical derivation of entanglement entropy and charge fluctuations for Dirac fermions, confirming their universality and exploring geometric effects.

Findings

Entanglement entropy matches conformal field theory predictions.

Charge variance exhibits the same asymptotic behavior as EE.

Flux response is geometry-independent as long as flux is enclosed.

Abstract

We investigate the entanglement entropy (EE) and charge fluctuations in models where the low energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, \emph{i.e.}, independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and number of Dirac cones, and either for strictly two-dimensional models or for gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides non-universal, geometry dependent results.