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.

Communications in Theoretical PhysicsFeb 1, 20115 citations

arXiv:0806.1369 · Annals of Physics

Berry phase and quantum criticality in Yang–Baxter systems

Jing‐Ling Chen, Kang Xue, Mo‐Lin Ge

Published Jun 15, 2008• 52 citations

arXiv HTML PDF

DOI: 10.1016/j.aop.2008.06.003

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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.