  In some spin tunneling problems, there are several different but
symmetry-related tunneling paths that connect the same initial and final
configurations. The topological phase factors of the corresponding tunneling
amplitudes can lead to destructive interference between the different paths, so
that the total tunneling amplitude is zero. In the study of tunneling between
different ground state configurations of the Kagom\'{e}-lattice quantum
Heisenberg antiferromagnet, this occurs when the spin $s$ is half-odd-integer.

Condensed Matter