PIRSA:15120030

Tensor networks for topological quantum matter

Sahinoglu, B. (2015). Tensor networks for topological quantum matter. Perimeter Institute. https://pirsa.org/15120030

Sahinoglu, Burak. Tensor networks for topological quantum matter. Perimeter Institute, Dec. 14, 2015, https://pirsa.org/15120030 

          @misc{ pirsa_PIRSA:15120030,
            doi = {10.48660/15120030},
            url = {https://pirsa.org/15120030},
            author = {Sahinoglu, Burak},
            keywords = {Condensed Matter},
            language = {en},
            title = {Tensor networks for topological quantum matter},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {dec},
            note = {PIRSA:15120030 see, \url{https://pirsa.org}}
          }

Burak Sahinoglu

University of Vienna

Talk number
PIRSA:15120030
Collection
Talk Type
Subject
Abstract

In this talk, I present a new framework for topologically ordered gapped ground states in 2+1 spacetime dimensions (which generalizes to higher dimensions) using tensor networks. We will see that topological order can exist in tensor network states (TNS), if the local tensor satisfies certain axioms which we call MPO (matrix product operator)-injectivity and pulling through. We then continue with examples, and see how renormalization fixed point models in the literature (Levin-Wen models, etc.) can be covered in this framework. If time permits, we finish with a discussion of excitations and the generalization to higher dimensions.