Algebraic dynamic investigation for heterotrinuclear spin cluster

We investigate the heterotrinuclear trigonal spin cluster (each particle with S=1/2) driven by a time-dependent magnetic field. Using the method of algebraic dynamics, we calculate the non-adiabatic geometric phase or Berry phase and the degeneracy energy levels when the magnetic rotating around Z axis. Based on the exact analytical solutions, we show how the Berry phase depends on the external magnetic field parameters ω (the angular velocity of the rotating magnetic field) and θ (the angle between the magnetic field and Z axis), and discuss the changing diagram of the Berry phase of the system in the ground-state.