Factorized three-body S-matrix restrained by the Yang-Baxter equation and quantum entanglements

This paper investigates the physical effects of the 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 R̆123(θ,φ) 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 R̆(θ,φ)-matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed.