Universal signatures of Dirac fermions in entanglement and charge fluctuations

Crépel, Valentin; Hackenbroich, Anna; Regnault, Nicolas; Estienne, Benoit

doi:10.1103/physrevb.103.235108

Title: Universal signatures of Dirac fermions in entanglement and charge fluctuations

Journal Article · Wed Jun 02 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.235108· OSTI ID:1852148

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Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Max-Planck-Institute of Quantum Optics, Garching (Germany); Munich Center for Quantum Science and Technology, München (Germany)
Princeton Univ., NJ (United States); Sorbonne Univ., Paris (France); University Paris-Diderot (France)
Sorbonne Univ., Paris (France)

We study 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, 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 numbers of Dirac cones, and either for strictly two-dimensional models or for a 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 nonuniversal, geometry-dependent results.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0016239

OSTI ID:: 1852148

Journal Information:: Physical Review. B, Vol. 103, Issue 23; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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