Entanglement Spectra and Trace Index of Topological Insulators

          @misc{ pirsa_PIRSA:11090053,
            doi = {10.48660/11090053},
            url = {https://pirsa.org/11090053},
            author = {Hughes, Taylor},
            keywords = {Condensed Matter},
            language = {en},
            title = {Entanglement Spectra and Trace Index of Topological Insulators},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {sep},
            note = {PIRSA:11090053 see, \url{https://pirsa.org}}
          }
          

Abstract

We investigate the entanglement spectra of topological insulators which have gapless edge states on their 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 non-vanishing 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 in translationally invariant and disordered systems.