Using a dynamical cluster quantum Monte Carlo approximation, we investigate the d-wave superconducting transition temperature T c in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings tЈ and t in the form of a checkerboard pattern where t is the hopping within a 2 ϫ 2 plaquette, and tЈ is the hopping between the plaquettes. We find inhomogeneity suppresses T c . The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing T c , suggesting a strong correlation between these quantities.

Using a dynamical cluster quantum Monte Carlo approximation, we investigate the effect of local disorder on the stability of d-wave superconductivity including the effect of electronic correlations in both particle-particle and particle-hole channels. With increasing impurity potential, we find an initial rise of the critical temperature due to an enhancement of antiferromagnetic spin correlations, followed by a decrease of Tc due to scattering from impurity-induced moments and ordinary pairbreaking. We discuss the weak initial dependence of Tc on impurity concentration found in comparison to experiments on cuprates.

Dynamic path integral methods: A maximum entropy approach based on the combined use of real and imaginary time quantum Monte Carlo data Abstract. We present a pedagogical discussions of the dynamical mean field (DMFA) and dynamical cluster (DCA) approximations and associated Monte Carlo and entropy-based methods of Bayesian data analysis. The DMFA and DCA methods are developed as coarse-graining approximations and the relationship between the cluster and lattice problems are detailed. The Hirsch-Fye and continuous time Quantum Monte Carlo (QMC) algorithms are used to solve the cluster problem. The algorithms are discussed, together with methods for efiRcient measurements and the modifications required by the self-consistency of the DMFA/DCA. Then, several principles of Bayesian data analysis are presented. When coupled with information theory, this analysis produces a precise and systematic way to analytically continue Matsubara-time QMC results to real frequencies. We show how to use Bayesian inference to qualify the solution of the continuation and optimize the inputs. Besides developing the Bayesian formalism, we also present a detailed description of the data qualification, sketch an efficient algorithm to solve for the optimal spectra, give cautionary notes where appropriate, and present two detailed case studies to demonstrate the method.