Effects of entanglement on off-diagonal geometric phases

The effect of entanglement on off-diagonal geometric phases is investigated in the paper. Two spin-(1/2) particles in magnetic fields along the y direction are taken as an example. Three parameters (the purity of state r, the mixing angle θ and the relative phase β) are chosen to characterize the initial states. The nodal points at which the usual geometric phases disappear are calculated and illustrated as a function of the three parameters.