The Effect of Disorder on Strongly Correlated Electrons

This thesis is devoted to a study of the effect of disorder on strongly correlated electrons. For non-interacting electrons, Anderson localization occurs if the amount of disorder is sufficient. For disorder-free systems, a Mott metal-insulator transition may occur if the electron-electron interactions are strong enough. The question we ask in this thesis is what happens when both disorder and interactions are present. We study the Anderson-Hubbard model, which is the simplest model to include both interactions and disorder, using a Gutzwiller variational wave function (GWF) approach. We provide an assessment of how well this approach approximates the ground state of the model, using small chains which can be solved exactly. Except for the most strongly disordered systems, our GWF works very well in reproducing the ground-state energies, local charge densities, and spin-spin correlations. We then study Anderson localization of electrons from the response of the AndersonHubbard Hamiltonian to an external magnetic field. An Aharonov-Bohm flux induces a persistent current in mesoscopic rings, and we extract the localization length from the finite-size scaling of the current. We explore how the localization length depends on disorder strength and interaction strength. Strong interactions result in two competing tendencies: they tend to suppress the current because of strong correlations, and they also screen the disorder potential and ii making the system more homogenous. We find that, for strongly interacting electrons, the localization length may be large, even though the current is suppressed by strong correlations. This unexpected result highlights how strongly correlated materials can be quiet different from weakly correlated ones.