PIRSA:20110024 Conference Quantum Fields and Strings

DOI10.48660/20110024

Conference/School: Tensor Networks: from Simulations to Holography III

Bauer, A. (2020). A tensor-network approach to fixed-point models of topological phases. Perimeter Institute. https://pirsa.org/20110024

Bauer, Andreas. A tensor-network approach to fixed-point models of topological phases. Perimeter Institute, Nov. 17, 2020, https://pirsa.org/20110024 

@misc{ pirsa_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},
  year = {2020},
  month = {nov},
  note = {PIRSA:20110024 see, \url{https://pirsa.org}}
}

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."

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