Kitaev's Lattice Model and Turaev-Viro TQFTs

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.

LaTex2e with TikZ pictures; 29 pages

References in corpus (4)

• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Turaev-Viro invariants as an extended TQFT
• Braiding and entanglement in spin networks: a combinatorial approach to topological phases

Cited by in corpus (3)

• Quantum double aspects of surface code models
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras