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arXiv · 1506.00822

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

Holger Frahm·Nikos Karaiskos
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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.

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Holger Frahm, Nikos Karaiskos. 2015-06-02. Non-Abelian $SU(3)_k$ anyons: inversion identities for higher rank face models. https://doi.org/10.1088/1751-8113/48/48/484001

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