Kitaev's Lattice Model and Turaev-Viro TQFTs
arXiv:1206.2308
Abstract
In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Turaev-Viro theory on a surface with boundary.
arXiv commentLaTex2e with TikZ pictures; 29 pages
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- Kitaev's stabilizer code and chain complex theory of bicommutative Hopf algebras
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- Defects in Kitaev models and bicomodule algebras
- Mapping class group actions from Hopf monoids and ribbon graphs
- Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras
- Semidual Kitaev lattice model and tensor network representation
- A pair of homotopy-theoretic version of TQFT's induced by a Brown functor