  The checkerboard lattice, with alternating 'crossed' plaquettes, serves as
the two dimensional analog of the pyrochlore lattice. The corner sharing
plaquette structure leads to a hugely degenerate ground state, and no magnetic
order, for classical spins with short range antiferromagnetic interaction. For
the half-filled Hubbard model on this structure, however, we find that the Mott
insulating phase involves virtual electronic processes that generate longer
range and multispin couplings. These couplings lift the degeneracy, selecting a
'flux like' state in the Mott insulator. Increasing temperature leads,
strangely, to a sharp crossover from this state to a '120 degree' correlated
state and then a paramagnet. Decrease in the Hubbard repulsion drives the
system towards an insulator-metal transition - the moments reduce, and a spin
disordered state wins over the flux state. Near the insulator-metal transition
the electron system displays a pseudogap extending over a large temperature
window.
