Entanglement and Berry Phase in a (3×3)-dimensional Yang-Baxter System

Abstract

A 9×9 unitary $\breve{R}$ -matrix, solution of the Yang-Baxter Equation, is obtained in this paper. The entanglement properties of $\breve{R}$ -matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}$ -matrix acting on the standard basis. A Yang-Baxter Hamiltonian can be constructed from unitary $\breve{R}$ -matrix. Then the geometric properties of this system is studied. The results showed that the Berry phase of this system can be represented under the framework of SU(2) algebra.