Isometric Tensor Network States in Two Dimensions
APA
Zaletel, M. (2019). Isometric Tensor Network States in Two Dimensions. Perimeter Institute. https://pirsa.org/19040113
MLA
Zaletel, Michael. Isometric Tensor Network States in Two Dimensions. Perimeter Institute, Apr. 25, 2019, https://pirsa.org/19040113
BibTex
@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}} }
University of California, Berkeley
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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.