  We investigate the properties of the two-dimensional frustrated quantum
antiferromagnet on the square lattice, especially at infinitesimal doping. We
find that next nearest neighbor (N.N.) J2 and next-next N.N. J3 interactions
together destroy the antiferromagnetic long range order and stabilize a quantum
disordered valence bond crystalline plaquette phase. A static vacancy or a
dynamic hole doped into this phase liberates a spinon. From the profile of the
spinon wavefunction around the (static) vacancy we identify an intermediate
behavior between complete deconfinement (behavior seen in the kagome lattice)
and strong confinement (behavior seen in the checkerboard lattice) with the
emergence of two length scales, a spinon confinement length larger than the
magnetic correlation length. When a finite hole hopping is introduced, this
behavior translates into an extended (mobile) spinon-holon boundstate with a
very small quasiparticle weight. These features provide clear evidence for a
nearby "deconfined critical point" in a doped microscopic model. Finally, we
give arguments in favor of superconducting properties of the doped plaquette
phase.
