Universal signatures of Dirac fermions in entanglement and charge fluctuations

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.

Accepted in PRB

References in corpus (21)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Quantum Noise as an Entanglement Meter
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Universal terms for the entanglement entropy in 2+1 dimensions
• Entanglement Entropy in the O(N) model
• Universality of corner entanglement in conformal field theories
• Entanglement from Charge Statistics: Exact Relations for Many-Body Systems
• Towards measuring Entanglement Entropies in Many Body Systems
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement Hamiltonians for non-critical quantum chains
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Fractional Chiral Hinge Insulator
• Entropy of XY Spin Chain and Block Toeplitz Determinants
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Holographic torus entanglement and its RG flow
• Entanglement entropy as a witness of the Aharonov-Bohm effect in QFT

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• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Area-law entanglement from quantum geometry
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Holographic entanglement renormalisation for fermionic quantum matter
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator