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arXiv:0904.0092

Entanglement and Berry Phase in a $9\times 9$ Yang-Baxter system

Chunfang Sun, Gangcheng Wang, Kang Xue

Published Apr 1, 2009• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.0904.0092

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In this paper, we present reducible representation of the n2 braid group representation which is constructed on the tensor product of n-dimensional spaces. Specifically, it is shown that via a combining method, we can construct more n2 dimensional braiding S-matrices which satisfy the braid relations. By Yang–Baxterization approach, we derive a 9 × 9 unitary [Formula: see text]-matrix according to a 9 × 9 braiding S-matrix we have constructed. The entanglement properties of [Formula: see text]-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via [Formula: see text]-matrix acting on the standard basis.
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