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

A. Alexandradinata, Taylor L. Hughes, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

73 Scopus citations


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.

Original languageEnglish (US)
Article number195103
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number19
StatePublished - Nov 3 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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