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Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. In this talk I will present how virtual symmetries in tensor networks, summarized by the framework of matrix product operator (MPO) injectivity, are substantial to the classification of not only bosonic but also fermionic topological order in two dimensional systems. I will briefly discuss how this fact relates to Levin-Wen string net models and Tuarev-Viro state sum constructions. For the sake of concreteness, two examples of fermionic topological order, the fermionic toric code and the Majorana dimer model, are discussed using the language of fermionic tensor networks.

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Carolin Wille, FU Berlin
Seminar Room 0.03, ETP
Contact: Alex Altland