Abstract
In this paper, a 3 × 3-matrix representation of Birman---Wenzl---Murakami (BWM) algebra has been presented. Based on which, unitary matrices A(?, ? 1, ? 2) and B(?, ? 1, ? 2) are generated via Yang---Baxterization approach. A Hamiltonian is constructed from the unitary B(?, ?) matrix. Then we study Berry phase of the Yang---Baxter system, and obtain the relationship between topological parameter and Berry phase.
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