We explore the ground states and quantum phase transitions of two-dimensional, spin S = 1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and , Mod. Phys. Lett. B 4, 1043). The minimal model for square lattice antiferromagnets is a lattice discretization of the quantum nonlinear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with NΓ©el order at weak coupling and a confining paramagnetic ground state with bond charge (e.g., spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry groups is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring noncollinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S = 1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models. C 2002 Elsevier Science (USA) Εi β’ Ε j + β’ β’ β’ .
(1)
Here Ε j are S = 1/2 quantum spin operators on the sites, j, of a square lattice, the sum i j is over