Topological basis associated with B–M–W algebra: Two-spin-1/2 realization

Abstract In this letter, we study the two-spin-1/2 realization for the Birman–Murakami–Wenzl (B–M–W) algebra and the corresponding Yang–Baxter R ˘ ( θ , ϕ ) matrix. Based on the two-spin-1/2 realization for the B–M–W algebra, the three-dimensional topological space, which is spanned by topological basis, is investigated. By means of such topological basis realization, the four-dimensional Yang–Baxter R ˘ ( θ , ϕ ) can be reduced to Wigner D J function with J = 1 . The entanglement and Berry phase in the spectral parameter space are also explored. The results show that one can obtain a set of entangled basis via Yang–Baxter R ˘ ( θ , ϕ ) matrix acting on the standard basis, and the entanglement degree is maximum when the R ˘ i ( θ , ϕ ) turns to the braiding operator.

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