Abstract
We study the ground-state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping $t$ and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. By using the path-integral renormalization-group method, we study the phase diagram in the parameter space of the Hubbard interaction $U$ and the frustration-control parameter ${t}^{\ensuremath{'}}/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution, and the spin- and charge-correlation functions allow us to determine the phase diagram at zero temperature, at which the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.
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