We establish a generalization of Kitaev models based on unitary quantum groupoids. In particular, when inputting a Kitaev-Kong quantum groupoid $H_\mathcal{ C}$, we show that the ground state manifold of the generalized model is canonical isomorphic to that of the Levin-Wen model based on a unitary fusion category $\mathcal{ C}$. Therefore the generalized Kitaev models provide realizations of the target space of the Turaev-Viro TQFT based on $\mathcal{ C}$.
Categories: math.QA math-ph math.MP