A 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 $t'< t'_{\rm max}$ 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 $t'_{\rm max}$ 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 $t'=t'_{\rm max}$ is a factor of 2--6 smaller than the pairing temperature.