A 9×9 Matrix Representation of Birman--Wenzl--Murakami Algebra and BerryPhase in Yang-Baxter System

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理论物理通讯 ›› 2011, Vol. 55 ›› Issue (02) : 263-267.

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A 9×9 Matrix Representation of Birman--Wenzl--Murakami Algebra and BerryPhase in Yang-Baxter System

GOU Li-Dan,^1,2 XUE Kang,² and WANG Gang-Cheng²

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Abstract

We present a 9×9 S-matrix and E-matrix. A representation of specialized Birman-Wenzl-Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix \breve{R}(x,φ₁,φ₂) is generated via the
Yang-Baxterization approach. Then we construct a Yang-Baxter
Hamiltonian through the unitary matrix \breve{R}(x,φ₁,φ₂). Berry phase of this Yang-Baxter system is investigated in detail.

导出引用

GOU Li-Dan,, XUE Kang, and WANG Gang-Cheng. A 9×9 Matrix Representation of Birman--Wenzl--Murakami Algebra and BerryPhase in Yang-Baxter System[J]. 理论物理通讯, 2011, 55(02): 263-267

GOU Li-Dan,, XUE Kang, and WANG Gang-Cheng. A 9×9 Matrix Representation of Birman--Wenzl--Murakami Algebra and BerryPhase in Yang-Baxter System[J]. Communications in Theoretical Physics, 2011, 55(02): 263-267

中图分类号： 03.67.Mn 02.40.-k 03.65.Vf