Quadratic quantum antiferromagnets in the fermionic large-N limit

We show that SU(N) Heisenberg Hamiltonians with arbitrary-range quadratic antiferromagnetic couplings (i.e., H=(i,j)JijSi Sj0), with Jij>0) possess highly degenerate dimerized ground states in the fermionic infinite-N limit on a large class of lattices that includes all Bravais lattices in arbitrary dimension. These states break translational but not spin-rotational symmetry. © 1990 The American Physical Society.