The Berry phase of spin-j particle in q-deformed magnetic field and Wigner D-function

We investigate the Berry phase for quantum spin system in q-deformed magnetic field. Through the q-deformed Lie algebra, we found a set of magnetic field expressions which contain the parameter q. The Berry phase of the system could be adjusted by the parameter q. The corresponding general formula of the q-deformed Berry phase is presented for an arbitrary spin system. The same Hamiltonian can also be generated from the Wigner D-function which satisfies the Yang-Baxter equation