On the ground-state properties of antiferromagnetic half-integer spin   chains with long-range interactions
  The Lieb-Shultz-Mattis theorem is extended to Heisenberg chains with long-range interactions. We prove that the half-integer spin chain has no gap, if it possesses unique ground state and the exchange decays faster than the inverse-square of distance between spins. The results can be extended to a wide class of one-dimensional models. 
Tigran Hakobyan