Entanglement Spectra and Topological Insulators

          @misc{ pirsa_PIRSA:10050082,
            doi = {10.48660/10050082},
            url = {https://pirsa.org/10050082},
            author = {Hughes, Taylor},
            keywords = {},
            language = {en},
            title = {Entanglement Spectra and Topological Insulators},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050082 see, \url{https://pirsa.org}}
          }
          

Abstract

Recent work has explored some aspects of entanglement in topological insulators. Notably, the entanglement spectrum has been shown to mimic certain properties of the low-energy fermionic modes found on real spatial boundaries. I will discuss the many-body entanglement spectrum of topological insulators and show that it matches the expected CFT character structure that has been previously shown to hold in fractional quantum Hall effect ground states. I also present the analysis of a disorder-driven Anderson localization transition in a Chern-Insulator from an analysis of the entanglement spectrum. Interestingly, the disorder-averaged level-spacing statistics of the entanglement spectrum characterizes the system just as well as the statistics of the real energy spectrum, but with the advantage that only the ground state, and not the entire spectrum of excited states, needs to be calculated.