Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models

Abstract

We exhibit a mapping identifying Kitaev's quantum double lattice models explicitly as a subclass of Levin and Wen's string net models via a completion of the local Hilbert spaces with auxiliary degrees of freedom. This identification allows to carry over to these string net models the representation-theoretic classification of the excitations in quantum double models, as well as define them in arbitrary lattices, and provides an illustration of the abstract notion of Morita equivalence. The possibility of generalising the map to broader classes of string nets is considered.

8 pages, 6 eps figures; v2: matches published version

References in corpus (5)

• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Entanglement renormalization and topological order
• Explicit tensor network representation for the ground states of string-net models
• Exact entanglement renormalization for string-net models
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase