Hyper-invariant tensor networks and holography

          @misc{ scivideos_PIRSA:17040049,
            doi = {10.48660/17040049},
            url = {https://pirsa.org/17040049},
            author = {Evenbly, Glen},
            keywords = {Quantum Matter, Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Hyper-invariant tensor networks and holography},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040049 see, \url{https://scivideos.org/index.php/pirsa/17040049}}
          }
          

Abstract

I will propose a new class of tensor network state as a model for the AdS/CFT correspondence and holography. This class shall be demonstrated to retain key features of the multi-scale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS/CFT. Novel holographic features of this tensor network class will be examined, such as an equivalence between the causal cone C[R] and the entanglement wedge E[R] of connected boundary regions R.