Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models

Abstract

The spectral problem for an integrable system of particles satisfying the fusion rules of $SU(3{)}_k$ is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused $A_2^{(1)}$ interaction round a face (IRF) model of Jimbo, Miwa and Okado. The identities are proven using local properties of the Boltzmann weights, in particular the Yang-Baxter equation and unitarity. They are closely related to the consistency conditions for the construction of eigenvalues obtained in the Separation of Variables approach to integrable vertex models.

25 pages

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Cited by in corpus (4)

• Exact solution of the $D_3$ non-Abelian anyon chain
• Elaborating the phase diagram of spin-1 anyonic chains
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model
• Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday