Magnetic translation and Berry's phase factor through adiabatically rotating a magnetic field

Abstract

For a spin subjected to an adiabatically changing magnetic field, the solid angle result as embodied by a rotation operator is the only path-dependent factor in the quantum evolution operator. For a charged particle, the infinite degeneracy calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a path-ordered magnetic translation operator that enters into the evolution operator and determines the geometric phase. This result agrees with the fact that the instantaneous hamiltonian is invariant under magnetic translation as well as rotation. Experimental verification of the result is proposed.