Entanglement and Berry Phase in a $(3\times 3)-$dimensional Yang-Baxter system

Abstract

Based on the method which is given in Ref. [Sun et.al. arXiv:0904.0092v1], we present another $9\times 9$ unitary $\breve{R}-$matrix, solution of the Yang-Baxter Equation, is obtained in this paper. The entanglement properties of $\breve{R}-$matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}$-matrix acting on the standard basis. A Yang-Baxter Hamiltonian can be constructed from unitary $\breve{R}-$matrix. Then the geometric properties of this system is studied. The results showed that the Berry phase of this system can be represented under the framework of SU(2) algebra.

6 pages

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Cited by in corpus (7)

• Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate
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• Berry phase and entanglement of 3 qubits in a new Yang-Baxter system
• Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation
• ${\ell }_1$-norm and entanglement in screening out braiding from Yang-Baxter equation associated with ${\mathbb{Z}}_3$ parafermion
• Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem
• Yang-Baxter $\breve{R}$ matrix, Entanglement and Yangian