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arXiv · 1309.4181

Kitaev models based on unitary quantum groupoids

Liang Chang
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Abstract

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 $\mathcal{C}$.

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Liang Chang. 2014-01-01. Kitaev models based on unitary quantum groupoids. https://doi.org/10.1063/1.4869326

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