Berry Phases for Many-Spin Systems with Anisotropy Exchange Interaction in a Strong Magnetic Field

An approximate instantaneous eigenstate is presented for the many-spin system possessing the anisotropy exchange interaction in a strong magnetic field by the perturbation method. Based on the instantaneous eigenstate, the Berry phase of this state is worked out. Furthermore, the effect of the anisotropy exchange interaction on the Berry phase of the state for the many-spin system is studied.