  An extended Hubbard model (including nearest-neighbor repulsion and
antiferromagnetic spin exchange) is investigated on the frustrated checkerboard
lattice, a two-dimensional analog of the pyrochlore lattice. Combining
Gutzwiller renormalized mean-field (MF) calculations, exact diagonalization
(ED) techniques, and a weak-coupling renormalization group (RG) analysis we
provide strong evidence for a crystalline valence bond plaquette phase at
quarter-filling. The ground state is twofold degenerate and breaks translation
symmetry. The bond energies show a staggering while the charge distribution
remains uniform.
