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Based on the method which is given in Ref. [Sun et.al. arXiv:0904.0092v1], wepresent another $9\times 9$ unitary $\breve{R}-$matrix, solution of theYang-Baxter Equation, is obtained in this paper. The entanglement properties of$\breve{R}-$matrix is investigated, and the arbitrary degree of entanglementfor two-qutrit entangled states can be generated via $\breve{R}$-matrix actingon the standard basis. A Yang-Baxter Hamiltonian can be constructed fromunitary $\breve{R}-$matrix. Then the geometric properties of this system isstudied. The results showed that the Berry phase of this system can berepresented under the framework of SU(2) algebra.

Entanglement and Berry Phase in a $(3\times 3)-$dimensional Yang-Baxter system