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We investigate the influence of diagonal and off-diagonal disorder potentials on superconductivity in an attractive Hubbard model. The study is motivated by recent experimental and theoretical interest in understanding the microscopic mechanism by which impurities destroy superconductivity. In order to capture the spatial correlations accurately, we make use of the real-space Bogoliubov-de Gennes mean field method. We find that the response of a superconductor to disorder crucially depends, even qualitatively, on the type of disorder considered. Superconductivity is suppressed spatially homogeneously by off-diagonal (kinetic) disorder in comparison to the suppression by diagonal (potential) disorder which proceeds via the formation of strongly superconducting islands. Moreover, the non-superconducting phase is gapless in the case of kinetic disorder, suggesting a fermionic superconductor-insulator transition (SIT). This is in sharp contrast to the SIT tuned by diagonal disorder, which is understood to be bosonic in nature. A qualitatively distinct mechanism that allows for a BCS-like suppression of superconductivity with increasing disorder is, in fact, consistent with recent experiments on amorphous Bi films.

We compute the magnetic susceptibilities of interacting electrons in the presence of disorder on a two-dimensional square lattice by means of quantum Monte Carlo simulations. Clear evidence is found that at sufficiently low temperatures disorder can lead to an enhancement of the ferromagnetic susceptibility. We show that it is not related to the transition from a metal to an Anderson insulator in two dimensions, but is a rather general low-temperature property of interacting, disordered electronic systems.

The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two non-perturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and Quantum Monte Carlo. We find distinctive evidence for a zero-energy anomaly which is robust upon variation of doping, disorder and interaction strength. Its similarities to, and differences from, pseudogap formation in other contexts, including perturbative treatments of interactions and disorder, classical theories of localized charges, and in the clean Hubbard model, are discussed., Comment: 4.2 pages, 4 figures

In this paper we present a determinant quantum monte carlo study of the two dimensional Hubbard model with random site disorder. We show that, as in the case of bond disorder, the system undergoes a transition from an Anderson insulating phase to a metallic phase as the onsite repulsion U is increased beyond a critical value U_c. However, there appears to be no sharp signal of this metal-insulator transition in the screened site energies. We observe that, while the system remains metallic for interaction values upto twice U_c, the conductivity is maximal in the metallic phase just beyond U_c, and decreases for larger correlation., 6 pages, 10 eps figures, Revtex4

The properties of LiHoF$_4$ are believed to be well described by a long-range dipolar Ising model. We go beyond mean-field theory and calculate the phase diagram of the Ising model in a transverse field using a quantum Monte Carlo method. The relevant Ising degrees of freedom are obtained using a non-perturbative projection onto the low-lying crystal field eigenstates. We explicitly take the domain structure into account, and the strength of the near-neighbor exchange interaction is obtained as a fitting parameter. The on-site hyperfine interaction is approximately taken into account through a renormalization of the transverse applied magnetic field. Finally, we propose a spectroscopy experiment to precisely measure the most important parameter controlling the location of the phase boundary., Comment: 15 pages, 8 figures : Minor typos corrected. Refs. 8 and 28 added

Motivated by the rapidly growing possibilities for experiments with ultracold atoms in optical lattices we investigate the thermodynamic properties of correlated lattice fermions in the presence of an external spin-dependent random potential. The corresponding model, a Hubbard model with spin-dependent local random potentials, is solved within dynamical mean-field theory. This allows us to present a comprehensive picture of the thermodynamic properties of this system. In particular, we show that for a fixed total number of fermions spin-dependent disorder induces a magnetic polarization. The magnetic response of the polarized system differs from that of a system with conventional disorder., 20 pages, 11 figures, published version