Lieb-Schultz-Mattis theorem with long-range interactions

The Lieb-Schultz-Mattis theorem states that a finite-range Hamiltonian in translationally and spin-rotationally invariant spin-1/2 systems cannot have a unique gapped ground state. Here, the author extends the theorem to include Hamiltonians with terms that act on a finite number of sites, but which may be far apart, provided that the interaction strength decays with distance faster than a certain power law. As the spatial dimension increases, the power law required to guarantee the result demands faster decay.