Instability of plaquette valence-bond crystal phase in planar pyrochlore electron system

We study a geometrically frustrated Hubbard model on the checkerboard lattice with nearest neighbor (t) and diagonal (t^′) hoppings. By using the path-integral renormalization group method, we calculate the double occupancy and the plaquette singlet correlation function to discuss the instability of the plaquette valence-bond crystal (P-VBC) phase at half filling. It is found that the increase of Coulomb interaction induces a first-order Mott transition to the plaquette singlet insulating (PSI) phase for t^′ / t = 1.0, which naturally leads to the P-VBC phase in the Heisenberg limit. For t^′ / t = 0.8, the double quantum phase transitions occur, and the PSI phase is stabilized between paramagnetic metallic and antiferromagnetic insulating phase.