Topologically Quenched Tunnel Splitting in Spin Systems without Kramers' Degeneracy

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Abstract
Spin systems can undergo quantum tunneling with classically degenerate minima. In some cases, the amplitudes from symmetry-related trajectories can interfere destructively, quenching the tunneling rate. This quenching need not be related to Kramers' degeneracy. This is shown by studying a problem (relevant to macroscopic quantum phenomena in ferromagnetic particles) with biaxial symmetry and an external field. The tunnel splitting is found to oscillate with the field, vanishing at certain values. Spin path integrals are used to prove Kramers' theorem, and an extension in which a subset of the energy levels is systematically doubly degenerate.