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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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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 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)]).
Publication Date: 15-May-2018
Electronic Publication Date: 10-May-2018
Citation: Zheng, 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.97.195118
DOI: doi:10.1103/PhysRevB.97.195118
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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