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Trace index and spectral flow in the entanglement spectrum of topological insulators

Author(s): Alexandradinata, A; Hughes, Taylor L; Bernevig, Bogdan A

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Abstract: We investigate the entanglement spectra of topological insulators, which manifest edge states on a lattice with spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the single-particle entanglement spectrum, which we call a “trace index.” We find that any free-fermion topological insulator that exhibits spectral flow has a nonvanishing trace index, which provides us with a new description of topological invariants. In addition, we identify the signatures of spectral flow in the single-particle and many-body entanglement spectrum; in the process we present new methods to extract topological invariants and establish a connection between entanglement and quantum Hall physics.
Publication Date: 3-Nov-2011
Citation: Alexandradinata, A, Hughes, Taylor L, Bernevig, B Andrei. (2011). Trace index and spectral flow in the entanglement spectrum of topological insulators. PHYSICAL REVIEW B, 84 (10.1103/PhysRevB.84.195103
DOI: doi:10.1103/PhysRevB.84.195103
ISSN: 1098-0121
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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