Non-Abelian $SU(3)_k$ anyons: inversion identities for higher rank face models
- Resource Type
- Working Paper
- Authors
- Frahm, Holger; Karaiskos, Nikos
- Source
- j. Phys. A: Math. Theor. 48 (2015) 484001
- Subject
- Condensed Matter - Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
- Language
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.
Comment: 25 pages