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

Understand

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.