SPIN-PEIERLS, VALENCE-BOND SOLID, AND NEEL GROUND-STATES OF LOW-DIMENSIONAL QUANTUM ANTIFERROMAGNETS

We examine large-N limits of the nearest-neighbor SU(N) quantum antiferromagnets on bipartite lattices in d=1,2. In d=2 the model displays a transition from a Néel to a disordered phase. The properties of the disordered phase close to the phase boundary are crucially dependent upon the nature of hedgehog-like instanton tunneling events. We calculate the Berry phases of the instantons and show that, at scales larger than the spin-correlation length, the system can be described by a Coulomb plasma of instantons with complex fugacities. The properties of the Coulomb plasma vary periodically with the spin nc of the states at each site, with periodicity given by the coordination number Z of the lattice [nc=2S for SU(2)]. For nc 0 (mod Z) the disordered phase has a broken lattice symmetry with spin-Peierls order, while for nc=0 (mod Z), the ground state is a valence-bond solid state with no broken symmetry. Related topological effects for the d=1 chain lead to spin-Peierls order for odd nc. These results are for a class of models which have, at sites of the A sublattice, representations of SU(N) described by a Young tableau with a single row, and the conjugate on the B sublattice. Similar results are also obtained for representations with m rows, using U(m) gauge theory. © 1990 The American Physical Society.