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arXiv · 1404.4794

Topological Basis Associated with B-M-W algebra: Two Spin-1/2 Realization

Gangcheng Wang·Kang Xue·Chunfang Sun·Bo Liu·Ying Liu·Yan Zhang
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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 $\breve{R}(θ,ϕ)$ 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 $\breve{R}(θ,ϕ)$ 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 $\breve{R}(θ,ϕ)$ matrix acting on the standard basis, and the entanglement degree is maximum when the $\breve{R}_{i}(θ,ϕ)$ turns to the braiding operator.

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Gangcheng Wang, Kang Xue, Chunfang Sun, Bo Liu, Ying Liu, Yan Zhang. 2014-04-23. Topological Basis Associated with B-M-W algebra: Two Spin-1/2 Realization. https://doi.org/10.1016/j.physleta.2014.10.037

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