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

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

2009-07-15

arxiv.org/abs/0907.2670v2

Phys. Rev. B 80, 155136 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

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

Scientific paper

10.1103/PhysRevB.80.155136

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.

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