Entanglement Spectrum from Geometry

          @misc{ pirsa_PIRSA:11120042,
            doi = {10.48660/11120042},
            url = {https://pirsa.org/11120042},
            author = {Swingle, Brian},
            keywords = {Condensed Matter},
            language = {en},
            title = {Entanglement Spectrum from Geometry},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {dec},
            note = {PIRSA:11120042 see, \url{https://pirsa.org}}
          }
          

Abstract

The entanglement spectrum denotes the eigenvalues of the reduced density matrix of a region in the ground state of a many-body system. Given these eigenvalues, one can compute the entanglement entropy of the region, but the full spectrum contains much more information. I will review geometric methods to extract this spectrum for special subregions in lorentz and conformally invariant field theories (and any theory whose universal low energy physics is captured by such a field theory). Using this technology, I give a new proof that the entanglement spectrum in quantum hall states is the same as that of a physical edge. I will discuss a number of other applications of the formalism, including, if there is time, a more complicated calculation of universal terms in the entanglement entropy at certain deconfined quantum critical points. The ultimate messages are that geometry is intimately bound up with entanglement and that the entanglement cut should be viewed as a physical cut.