Hyper-invariant tensor networks and holography


Evenbly, G. (2017). Hyper-invariant tensor networks and holography. Perimeter Institute. https://pirsa.org/17040049


Evenbly, Glen. Hyper-invariant tensor networks and holography. Perimeter Institute, Apr. 21, 2017, https://pirsa.org/17040049


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

Glen Evenbly Georgia Institute of Technology


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.