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

TL;DR

This paper introduces a new 9x9 unitary R-matrix solution to the Yang-Baxter equation, explores its entanglement properties, constructs a related Hamiltonian, and analyzes the Berry phase within an SU(2) framework.

Contribution

It presents a novel unitary R-matrix for a 3x3 system, investigates its entanglement, and studies the geometric Berry phase, extending previous methods.

Findings

Arbitrary entanglement degrees can be generated using the R-matrix.

The Berry phase can be expressed within the SU(2) algebra framework.

A Yang-Baxter Hamiltonian related to the R-matrix is constructed.

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.