Entanglement and Berry phase in a 9 × 9 Yang–Baxter system

Abstract

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang---Baxterization approach, we obtain a unitary solution $${\breve{R}(\theta,\varphi_{1},\varphi_{2})}$$ 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 $${\varphi_{1}\,{=}\,\varphi_{2}}$$ , 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.