Excitation spectrum of the anisotropic generalization of an $SU_3$ magnet

The spectrum of an exactly solvable quantum-mechanical system on a chain with three-dimensional state space at a site is investigated. The system is related to the solution of the Yang–Baxter equations found by tzergin and Korepin. A new analytic method is used to find the eigenvatues of the generating function of the quantum integrals of the motion of the system. The thermodynamic limit over the antiferromagnetie ground state is considered.