Kitaev models based on unitary quantum groupoids

Source abstract

We establish a generalization of Kitaev models based on unitary quantum groupoids. In particular, when inputting a Kitaev-Kong quantum groupoid \documentclass[12pt]{minimal}\begin{document}$H_\mathcal {C}$\end{document}HC, we show that the ground state manifold of the generalized model is canonically isomorphic to that of the Levin-Wen model based on a unitary fusion category \documentclass[12pt]{minimal}\begin{document}$\mathcal {C}$\end{document}C. Therefore, the generalized Kitaev models provide realizations of the target space of the Turaev-Viro topological quantum field theory based on \documentclass[12pt]{minimal}\begin{document}$\mathcal {C}$\end{document}C.