Abstract
We present a 9 × 9 S-matrix and E-matrix. A representation of specialized Birman—Wenzl—Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix Ř(x, ϕ1,ϕ2) is generated via the Yang—Baxterization approach. Then we construct a Yang—Baxter Hamiltonian through the unitary matrix Ř(x, ϕ1,ϕ2). Berry phase of this Yang—Baxter system is investigated in detail.
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