Communications in Theoretical Physics

A 9 × 9 Matrix Representation of Birman—Wenzl—Murakami Algebra and Berry Phase in Yang—Baxter System

Lidan Gou, Kang Xue, Gangcheng Wang

Published Feb 1, 2011• 5 citations

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 Ř(x, ϕ 1 ,ϕ 2 ) is generated via the Yang—Baxterization approach. Then we construct a Yang—Baxter Hamiltonian through the unitary matrix Ř(x, ϕ 1 ,ϕ 2 ). Berry phase of this Yang—Baxter system is investigated in detail.

DOI: 10.1088/0253-6102/55/2/14

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Communications in Theoretical Physics

A 9 × 9 Matrix Representation of Birman—Wenzl—Murakami Algebra and Berry Phase in Yang—Baxter System

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Published Feb 1, 2011• 5 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/55/2/14

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Entanglement and Berry Phase in a

9\times 9

Yang-Baxter system

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang-Baxterization approach, we obtain a unitary solution

\breve{R}(θ,φ_{1},φ_{2})

of Yang-Baxter Equation. It is shown that any pure two-qutrit entangled states can be generated via the universal

\breve{R}

-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the

\breve{R}

-matrix, and Berry phase of the Yang-Baxter system is investigated. Specifically, for $ φ_{1}=φ_{2}$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.