Determinant Quantum Monte Carlo Study of d-wave pairing in the Plaquette Hubbard Hamiltonian

Determinant Quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters -a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping $t$ and on-site repulsion $U$ coupled by an inter-plaquette hopping $t' \leq t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For $U/t=4$, DQMC indicates an optimal $t'/t \approx 0.4$ at which the pairing vertex is most attractive. The optimal $t'/t$ increases with $U/t$. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO$_2$ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.