Hardcore bosons on checkerboard lattices near half filling: geometric   frustration, vanishing charge order and fractional phase
  We study a spinless hardcore boson model on checkerboard lattices by Green function Monte Carlo method. At half filling, the ground state energy is obtained up to $28\times 28$ lattice and extrapolated to infinite size, the staggered pseudospin magnetization is found to vanish in the thermodynamic limit. Thus the $(\pi,\pi)$ charge order is absent in this system. Away from half filling, two defects induced by each hole (particle) may carry fractional charge ($\pm e/2$). For one hole case, we study how the defect-defect correlation changes with $t/J$, which is the ratio between the hopping integral and cyclic exchange, equals to $V/2t$ when $V\gg t$. Moreover, we argue that these fractional defects may propagate independently when the concentration of holes (or defects) is large enough. 
Yi Zhou