Integrable anyon chains

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In this project we plan to construct integrable chains of interacting non-Abelian anyons and study the spectrum and thermodynamic properties, in particular their critical behaviour. Unlike in the more conventional approach using a quantum spin formulation of these chains we shall focus on the anyonformulation. This allows to deal with quantum systems with non-integer quantum dimension which have no natural tensor product structure on their Hilbert space.First, we shall deal with two specific species of anyons with an internal symmetry related to the dihedral group D3. Up to boundary conditions the integrable anyon chains for these objects are equivalent to quantum spin chains showing this symmetry. The properties of the latter are well-studied, thereby allowing a direct comparison of the properties of these objects in the different formulations.In another part of this project we plan to combine the techniques developed here into a framework which can be used to construct and solve anyonic chains with generic internal symmetries.