New Integrable Deformations of Higher Spin Heisenberg-Ising Chains

Abstract

We show that the anisotropic Heisenberg-Ising chains with higher spin allow, for special values of the anisotropy, integrable deformations intimately related to the theory of quantum groups at roots of unity. For the spin one case we construct and study the symmetries of the hamiltonian which depends on a spectral variable belonging to an elliptic curve. One of the points of this curve yields the Fateev-Zamolodchikov hamiltonian of spin one and anisotropy $\Delta = \frac{ q^2 + q^{-2}}{2} $ with $q$ a cubic root of unity. In some other special points the spin degrees of freedom as well as the hamiltonian splits into pieces governed by a larger symmetry.