Plaquette bond order wave in the quarter-filled extended Hubbard model   on the checkerboard lattice
  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. 
Martin Indergand, Carsten Honerkamp, Andreas Laeuchli, Didier   Poilblanc and Manfred Sigrist