Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter

Yunqin Zheng, Huan He, Barry Bradlyn, Jennifer Cano, Titus Neupert, and B. Andrei Bernevig
Phys. Rev. B 97, 195118 – Published 10 May 2018

Abstract

We study the entanglement entropy of gapped phases of matter in three spatial dimensions. We focus in particular on size-independent contributions to the entropy across entanglement surfaces of arbitrary topologies. We show that for low energy fixed-point theories, the constant part of the entanglement entropy across any surface can be reduced to a linear combination of the entropies across a sphere and a torus. We first derive our results using strong sub-additivity inequalities along with assumptions about the entanglement entropy of fixed-point models, and identify the topological contribution by considering the renormalization group flow; in this way we give an explicit definition of topological entanglement entropy Stopo in (3+1)D, which sharpens previous results. We illustrate our results using several concrete examples and independent calculations, and show adding “twist” terms to the Lagrangian can change Stopo in (3+1)D. For the generalized Walker-Wang models, we find that the ground state degeneracy on a 3-torus is given by exp(3Stopo[T2]) in terms of the topological entanglement entropy across a 2-torus. We conjecture that a similar relationship holds for Abelian theories in (d+1) dimensional spacetime, with the ground state degeneracy on the d-torus given by exp(dStopo[Td1]).

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
9 More
  • Received 11 October 2017

DOI:https://doi.org/10.1103/PhysRevB.97.195118

©2018 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yunqin Zheng1, Huan He1, Barry Bradlyn2, Jennifer Cano2, Titus Neupert3, and B. Andrei Bernevig1,4,5,6,*

  • 1Physics Department, Princeton University, Princeton, New Jersey 08544, USA
  • 2Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 3Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
  • 4Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
  • 5Laboratoire Pierre Aigrain, Ecole Normale Superieure-PSL Research University, CNRS, Universite Pierre et Marie Curie-Sorbonne Universites, Universite Paris Diderot-Sorbonne Paris Cite, 24 rue Lhomond, 75231 Paris Cedex 05, France
  • 6Sorbonne Universites, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris, France

  • *On sabbatical.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 97, Iss. 19 — 15 May 2018

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×