Algebraic dynamics study for homotrinuclear linear spin cluster in a rotating magnetic field

Abstract

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 $\ensuremath{\omega}$ and $\ensuremath{\theta}$ has been determined by using the relation between the Berry phase and the angular velocity $\ensuremath{\omega}$ of the rotating magnetic field as well as the angle $\ensuremath{\theta}$ between the magnetic field and $Z$ axis. We obtain the changing diagram of the Berry phase of the basis state.