$A_2^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation

Abstract

The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_2^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.

arXiv comment20 pages,no figure, typos corrected, LaTex

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Cited by in corpus (3)

• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models
• $osp(1|2)$ off-shell Bethe ansatz equation with boundary terms