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

## Author(s): Zheng, Yunqin; He, Huan; Bradlyn, Barry; Cano, Jennifer; Neupert, Titus; et al

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dc.contributor.authorZheng, Yunqin-
dc.contributor.authorHe, Huan-
dc.contributor.authorCano, Jennifer-
dc.contributor.authorNeupert, Titus-
dc.contributor.authorBernevig, Bogdan A.-
dc.date.accessioned2019-12-10T15:59:13Z-
dc.date.available2019-12-10T15:59:13Z-
dc.date.issued2018-05-15en_US
dc.identifier.citationZheng, Yunqin, He, Huan, Bradlyn, Barry, Cano, Jennifer, Neupert, Titus, Bernevig, B Andrei. (2018). Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter. PHYSICAL REVIEW B, 97 (10.1103/PhysRevB.97.195118en_US
dc.identifier.issn2469-9950-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1tx8j-
dc.description.abstractWe 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 S-topo 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 S-topo 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(-3S(topo) [T-2]) 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(-dS(topo) [Td(-1)]).en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW Ben_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleStructure of the entanglement entropy of (3+1)-dimensional gapped phases of matteren_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevB.97.195118-
dc.date.eissued2018-05-10en_US
dc.identifier.eissn2469-9969-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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