Carolin Wille

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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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FU Berlin
Seminar Room 0.03, ETP
Contact: Alex Altland