Kitaev models based on unitary quantum groupoids

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 $\mathcal{C}$.

Revised version, 22 pages

References in corpus (4)

• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Turaev-Viro invariants as an extended TQFT
• Kitaev's Lattice Model and Turaev-Viro TQFTs
• (3+1)-TQFTs and Topological Insulators

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• A unified diagrammatic approach to topological fixed point models
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• Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs
• Generating domain walls between topologically ordered phases using quantum double models
• Toric code-like models from the parameter space of $3D$ lattice gauge theories
• Quantum Double Models coupled to matter fields: a detailed review for a dualization procedure