  A M-matrix which satisfies the Hecke algebraic relations is presented. Via
the Yang-Baxterization approach, we obtain a unitary solution
$\breve{R}(\theta,\varphi_{1},\varphi_{2})$ of Yang-Baxter Equation. It is
shown that any pure two-qutrit entangled states can be generated via the
universal $\breve{R}$-matrix assisted by local unitary transformations. A
Hamiltonian is constructed from the $\breve{R}$-matrix, and Berry phase of the
Yang-Baxter system is investigated. Specifically, for $
\varphi_{1}=\varphi_{2}$, the Hamiltonian can be represented based on three
sets of SU(2) operators, and three oscillator Hamiltonians can be obtained.
Under this framework, the Berry phase can be interpreted.

Quantum Physics