  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 Jalabert (Mod. Phys. Lett. B
4, 1043 (1990), http://onsager.physics.yale.edu/p32.pdf). The `minimal' model
for square lattice antiferromagnets is a lattice discretization of the quantum
non-linear 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 Neel 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 group 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 non-collinear, 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.
