Geometric phase and entanglement for massive spin-1 particles

The cyclic evolution of a spin-1 system is studied under the spin-spin interaction between the transverse and the longitudinal states. The eigenstates of the systems are obtained by generalized and extended Jordan-Wigner transformation with an angle ϕ described the path of particle propagation. According to the wave functions of time evaluation for many-particle systems, the entanglement effects and geometric phase are observed. The systems with more than two particles, in contrast to the two particle system, evolve in time with two parameters