Destructive quantum interference in spin tunneling problems

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.