PIRSA:19040113

Isometric Tensor Network States in Two Dimensions

Zaletel, M. (2019). Isometric Tensor Network States in Two Dimensions. Perimeter Institute. https://pirsa.org/19040113

Zaletel, Michael. Isometric Tensor Network States in Two Dimensions. Perimeter Institute, Apr. 25, 2019, https://pirsa.org/19040113 

          @misc{ pirsa_PIRSA:19040113,
            doi = {10.48660/19040113},
            url = {https://pirsa.org/19040113},
            author = {Zaletel, Michael},
            keywords = {Condensed Matter},
            language = {en},
            title = {Isometric Tensor Network States in Two Dimensions},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {apr},
            note = {PIRSA:19040113 see, \url{https://pirsa.org}}
          }

Michael Zaletel University of California, Berkeley

DOI 10.48660/19040113
Collection
Talk Type Conference
Subject

Abstract

We introduce an isometric restriction of the tensor-network ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D tensor network. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD2) for approximating the ground state of a Hamiltonian as an isometric tensor network, which we demonstrate for the 2D transverse field Ising model.