Contractor-renormalization study of Hubbard plaquette clusters

We implement the contractor-renormalization method to study the checkerboard Hubbard model on various finite-size clusters as function of the inter-plaquette hopping t^′ and the on-site repulsion U at low hole doping. We find that the pair-binding energy and the spin gap exhibit a pronounced maximum at intermediate values of t^′ and U, thus indicating that moderate inhomogeneity of the type considered here substantially enhances the formation of hole pairs. The rise of the pair-binding energy for t^′ < t max ′ is kinetic-energy driven and reflects the strong resonating valence-bond correlations in the ground state that facilitate the motion of bound pairs as compared to single holes. Conversely, as t ^′ is increased beyond t max ′ antiferromagnetic magnons proliferate and reduce the potential energy of unpaired holes and with it the pairing strength. For the periodic clusters that we study the estimated phase-ordering temperature at t^′ = t max ′ is a factor of 2-6 smaller than the pairing temperature.