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

• We study a two-spin-1/2 realization of Birman–Murakami–Wenzl algebra.
• Topological basis for this model is constructed in this paper.
• The reduced representation is related with Wigner D matrix.

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 DJDJ function with J=1J=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.