New Integrable Deformations of Higher Spin Heisenberg-Ising Chains

TL;DR

This paper introduces new integrable deformations of higher spin Heisenberg-Ising chains, revealing special anisotropy values linked to quantum groups at roots of unity and exploring their symmetries and spectral properties.

Contribution

It constructs and analyzes integrable deformations of higher spin chains related to quantum groups at roots of unity, including explicit symmetry and Hamiltonian structures.

Findings

Identification of special anisotropy points related to quantum groups at roots of unity.

Construction of Hamiltonians with elliptic curve spectral parameters.

Discovery of enhanced symmetries at specific points.

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.