A theorem on the existence of a gap in the energy spectrum of quantum systems, the exact ground state of which is known explicitly, is proved. The theorem is applied to a three-dimensional Heisenberg spin-1/2 ferromagnet, with anisotropic nearest-neighbour interactions, and to an alternating Heisenberg antiferromagnet, with nearest- and next-nearest-neighbour interactions.
Caspers, W. J., & Magnus, W. (1983). On the existence of a gap in the energy spectrum of quantum systems. Journal of Physics C: Solid State Physics, 16(33), 6395. https://doi.org/10.1088/0022-3719/16/33/012