Abstract
In this paper, a (3\times3)-matrix representation of the Birman-Wenzl-Murakami(BWM) algebra has been presented. Based on which, unitary matrices (A(θ,ϕ_1,ϕ_2), B(θ,ϕ_1,ϕ_2)) are generated via the Yang-Baxterization approach. A hamiltonian is constructed from the unitary (B(θ,ϕ)) matrix. We then study the Berry phase of the Yang-Baxter system and find the topological parameter d has relationship with berry phase.
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