Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets

The large-N limit of a nearest-neighbor SU (N) antiferromagnet on a bipartite lattice exhibits in dimensions d2 a zero-temperature phase transition between a N\'eel ordered state and a resonating-valence-bond state. Here it is shown in d=1, 2 that topological effects produce spin-Peierls or valence-bond-solid order in the non-N\'eel phase with a ground-state degeneracy which varies periodically with ``spin'' for fixed N with periodicity given by the coordination number of the lattice. Thus a non-N\'eel phase of the spin- (1/2 Heisenberg model on a square lattice would be a spin-Peierls state with a fourfold degeneracy due to broken lattice rotational symmetry.