Effect of Aharonov-Bohm phase on spin tunneling

The role of Aharonov-Bohm effect in quantum tunneling is examined when a potential is defined on the S-1 and has N-fold symmetry. We show that the low-lying energy levels split from the N-fold degenerate ground state oscillate with the Aharonov-Bohm phase, from which general degeneracy conditions depending on the magnetic flux is obtained. We apply these results to the spin tunneling in a spin system with N-fold rotational symmetry around a hard axis.