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

TL;DR

This paper establishes an explicit mapping from Kitaev's quantum double models to Levin and Wen's string-net models, enabling the transfer of classification methods and generalizations across these frameworks.

Contribution

It provides a concrete construction linking quantum double and string-net models, illustrating Morita equivalence and facilitating broader applicability.

Findings

Mapping explicitly identifies quantum double models as a subclass of string-net models

Allows transfer of excitation classification from quantum doubles to string-nets

Enables generalization of the mapping to other string-net classes

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.