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We study a spinless hardcore boson model on checkerboard lattices by Greenfunction Monte Carlo method. At half filling, the ground state energy isobtained up to $28\times 28$ lattice and extrapolated to infinite size, thestaggered pseudospin magnetization is found to vanish in the thermodynamiclimit. Thus the $(\pi,\pi)$ charge order is absent in this system. Away fromhalf filling, two defects induced by each hole (particle) may carry fractionalcharge ($\pm e/2$). For one hole case, we study how the defect-defectcorrelation changes with $t/J$, which is the ratio between the hopping integraland cyclic exchange, equals to $V/2t$ when $V\gg t$. Moreover, we argue thatthese fractional defects may propagate independently when the concentration ofholes (or defects) is large enough.

Hardcore bosons on checkerboard lattices near half filling: geometric frustration, vanishing charge order and fractional phase