We present results of three studies done using a dynamical cluster quantum Monte Carlo approximation. First, we investigate the d-wave superconducting transition temperature Tc in the doped 2D repulsive Hubbard model with a weak inhomogeneity in hopping in the form of checkerboard pattern or a lattice of 2×2 plaquettes. Near neighbor hoppings within a plaquette is t and that of between the plaquettes is t'. We investigate Tc in the weak inhomogeneous limit
0.8t < t'< 1.2t. We find inhomogeneity (t'≠ t) suppresses Tc. The characteristic spin excitation energy (effective exchange energy) and the strength of d-wave pairing interaction decrease with decreasing Tc. The latter observations suggest a strong correlation among effective exchange interaction, Tc and the d-wave pairing interaction of the system. Second*, we further find that enhancement of effective exchange interaction causes a slight increase in Tc of a weakly disordered system with low impurity concentration, compared to the homogeneous system. Here the disorder is introduced to homogeneous repulsive 2D Hubbard model as a weak local potential disorder. Third, we present an improved maximum entropy method to analytically continue quantum Monte Carlo data with a severe sign problem.
* A result from a collaborative study done with A. Kemper of Florida State University.