Dynamics and geometric phase of two spins with exchange coupling in a rotating magnetic field

An exact solution of time-dependent Schrödinger equation for two coupled spins of arbitrary values in a rotating magnetic field is obtained by means of a time-dependent gauge transformation technique which results in both exact and adiabatic geometric phases without the questionable request of remaining in the initial instantaneous eigenstate during the time-evolution. Thus our derivation of the Berry phase is free of inconsistency caused by the standard adiabatic theorem.