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Citation: Buerschaper, Oliver, and Miguel Aguado. "Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models." Physical Review B 80.15 (2009): 155136.
Tags: Non-abelian-anyons, Pedagogical
This paper explicitly connects the standard Kitaev lattice quantum double construction with the Levin-Wen string-net model. It also gives a very nice philosophical discussion of quantum double models, string-nets, and Mortia equivalence.
This mapping makes key use of the non-abelian Fourier transform, which is a key ingredient in what makes the quantum double theory "tick". Hence, this seems like a good paper to go to when trying to get to the key idea of the non-abelian Kitaev quantum double model.