Factorized Three-body S-Matrix Restrained by Yang-Baxter Equation and Quantum Entanglements

Abstract

This paper investigates the physical effects of Yang-Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix ${\breve{R}}_{123}(\theta ,\phi )$ based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the $\breve{R}(\theta ,\phi )$-matrix gives GHZ and W state respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed.

13 pages, 2 figures

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• ${\mathbb{Z}}_3$ Parafermionic Chain Emerging From Yang-Baxter Equation
• More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation
• New type of solutions of Yang-Baxter equations, quantum entanglement and related physical models