Quadratic quantum antiferromagnets in the fermionic large-Nlimit

We show that SU(N) Heisenberg Hamiltonians with arbitrary-range quadratic antiferromagnetic couplings (i.e., H=${\mathrm{\Sigma }}_{(\mathit{i},\mathit{j})}$ ${\mathit{J}}_{\mathit{ij}}$ ${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{j}}$≳0), with ${\mathit{J}}_{\mathit{i}\mathit{j}}$>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.