Using the method of dynamical algebras, the solution of a homotriparticle linear spin cluster (each particle with S=1/2) in a rotating magnetic field is obtained. We derive degeneracy energy levels and each level's Berry phase of this system. The Berry phase as a function of omega and theta has been determined by using the relation between the Berry phase and the angular velocity omega of the rotating magnetic field as well as the angle theta between the magnetic field and Z axis. We obtain the changing diagram of the Berry phase of the basis state.
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