A tensor-network approach to fixed-point models of topological phases

          @misc{ scivideos_PIRSA:20110024,
            doi = {10.48660/20110024},
            url = {https://pirsa.org/20110024},
            author = {Bauer, Andreas},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {A tensor-network approach to fixed-point models of topological phases},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2020},
            month = {nov},
            note = {PIRSA:20110024 see, \url{https://scivideos.org/pirsa/20110024}}
          }
          

Abstract

"I will introduce a tensor-network based language for classifying topological phases via fixed-point models. The "models" will be tensor networks formalizing a discrete Euclidean path integral living in a topological space-time, and can be obtained from Hamiltonian models by Trotterizing the imaginary time evolution. Topological fixed-point models are invariant under topology-preserving space-time deformations. Space-time manifolds and homeomorphisms can be combinatorially represented by graph-like "networks", which together with "moves" form a "liquid". The networks can be interpreted as tensor networks, and the moves as equations which determine the fixed-point models. Different combinatorial representations of the same space-times yield new kinds of fixed-point models. Given the limited time, I will stick to very simple examples in 1+1 dimensions for this talk."