1205.4614 (N. Grosjean et al.)

The tau_2-model and the chiral Potts model revisited: completeness of
Bethe equations from Sklyanin's SOV method    [PDF]

N. Grosjean, G. Niccoli

The most general cyclic representations of the quantum integrable tau_2-model are analyzed. The complete characterization of the tau_2-spectrum (eigenvalues and eigenstates) is achieved in the framework of Sklyanin's Separation of Variables (SOV) method by extending and adapting the ideas first introduced in the paper [1]: i) The determination of the tau_2-spectrum is reduced to the classification of the solutions of a given functional equation in a class of polynomials. ii) The determination of the tau_2-eigenstates is reduced to the classification of the solutions of an associated Baxter equation. These last solutions are proven to be polynomials for a quite general class of tau_2-self-adjoint representations and the completeness of the associated Bethe ansatz type equations is derived. Finally, the following results are derived for the inhomogeneous chiral Potts model: i) Simplicity of the spectrum, for general representations. ii) Complete characterization of the chiral Potts spectrum (eigenvalues and eigenstates) and completeness of Bethe ansatz type equations, for the self-adjoint representations of tau_2-model on the chiral Potts model algebraic curves.

View original: http://arxiv.org/abs/1205.4614