Integrable anyon chains: from fusion rules to face models to effective field theories

Abstract

Starting from the fusion rules for the algebra $SO(5{)}_2$ we construct one-dimensional lattice models of interacting anyons with commuting transfer matrices of `interactions round the face' (IRF) type. The conserved topological charges of the anyon chain are recovered from the transfer matrices in the limit of large spectral parameter. The properties of the models in the thermodynamic limit and the low energy excitations are studied using Bethe ansatz methods. Two of the anyon models are critical at zero temperature. From the analysis of the finite size spectrum we find that they are effectively described by rational conformal field theories invariant under extensions of the Virasoro algebra, namely $\mathcal{W}{B}_2$ and $\mathcal{W}{D}_5$, respectively. The latter contains primaries with half and quarter spin. The modular partition function and fusion rules are derived and found to be consistent with the results for the lattice model.

arXiv comment43 pages, published version

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• Exact solution of the $D_3$ non-Abelian anyon chain
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• 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
• Density matrices in integrable face models
• Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
• Condensates of interacting non-Abelian $SO(5{)}_{N_f}$ anyons