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

Abstract

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 a $28\ifmmode\times\else\texttimes\fi{}28$ lattice and extrapolated to infinite size; the staggered pseudospin magnetization is found to vanish in the thermodynamic limit. Thus the $(\ensuremath{\pi},\ensuremath{\pi})$ charge order is absent in this system. Away from half filling, two defects induced by each hole (particle) may carry fractional charge $(\ifmmode\pm\else\textpm\fi{}e∕2)$. For the 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, and is equal to $V∕2t$ when $V⪢t$. Moreover, we argue that these fractional defects may propagate independently when the concentration of holes (or defects) is large enough.