Exotic phenomena in doped quantum magnets

We investigate the properties of a two-dimensional frustrated quantum antiferromagnet on a square lattice, especially at infinitesimal doping. We find that next nearest neighbour (NN) J2 and next–next NN 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 behaviour between complete deconfinement (behaviour seen in the kagome lattice) and strong confinement (behaviour seen in the checkerboard lattice) with the emergence of two length scales, a spinon confinement length larger than the magnetic correlation length. When finite hole hopping is introduced, this behaviour translates into an extended (mobile) spinon–holon bound state 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 to support the idea that the doped plaquette phase has superconducting properties.