Tensor Network Renormalization and the MERA


Evenbly, G. (2015). Tensor Network Renormalization and the MERA. Perimeter Institute. https://pirsa.org/15080065


Evenbly, Glen. Tensor Network Renormalization and the MERA. Perimeter Institute, Aug. 18, 2015, https://pirsa.org/15080065


          @misc{ pirsa_PIRSA:15080065,
            doi = {10.48660/15080065},
            url = {https://pirsa.org/15080065},
            author = {Evenbly, Glen},
            keywords = {Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Tensor Network Renormalization and the MERA},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {aug},
            note = {PIRSA:15080065 see, \url{https://pirsa.org}}

Glen Evenbly Georgia Institute of Technology


I describe a class of non-perturbative renormalization group (RG) transformations which, when applied to the (discrete time) Euclidean path integrals of a quantum systems on the lattice, can give results consistent with conformal transformations of quantum field theories. In particular, this class of transformation, which we call Tensor Network Renormalization (TNR), is shown to generate a scale-invariant RG flow for quantum systems at a critical point. Applications of TNR towards study of quantum critical systems, and its relationship to the multi-scale-entanglement renormalization ansatz (MERA) for ground and thermal states of quantum systems, will be discussed.