The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra

Abstract

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group $D_3$ are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a $Z_4$ parafermion or a ${\mathcal{M}}_{(5,6)}$ minimal model.

Major revisions have been made

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Cited by in corpus (10)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Integrable anyon chains: from fusion rules to face models to effective field theories
• An integrable model with parafermion zero energy modes
• Exact solution of the $D_3$ non-Abelian anyon chain
• ${\mathbf{Z}}_n$ clock models and chains of $so(n{)}_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
• Russian doll spectrum in a non-Abelian string-net ladder
• Effective models of doped quantum ladders of non-Abelian anyons
• Elaborating the phase diagram of spin-1 anyonic chains
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models
• Factorization of density matrices in the critical RSOS models