Determinant quantum Monte Carlo study ofd-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 2×2 plaquettes with hopping t and on-site repulsion U coupled by an interplaquette hopping t^'≤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≈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 CuO₂ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.