Anderson Transitions and Interactions

In this report we present our study of disordered interacting systems. Our interest here is two-fold: we want to study superconductor-insulator-transition in disordered thin film superconductors and the many-body localization transition in interacting one-dimensional wires. Our main topic, disordered thin film superconductors, were modelled within a mean-field framework. We investigate the effect of full self-consistency (sc) on local observables within the Boguliubov-deGennes (BdG) theory of the attractive-U Hubbard model in the presence of on-site disorder; the sc-fields are the particle density $$n(\mathbf{r})$$ n ( r ) and the gap function $$\varDelta (\mathbf{r})$$ Δ ( r ) . For this case, we reach system sizes unprecedented in earlier work. They allow us to study phenomena emerging at scales substantially larger than the lattice constant, such as the interplay of multifractality and interactions, or the formation of superconducting islands. For example, we observe that the coherence length exhibits a non-monotonic behavior with increasing disorder strength already at moderate U. In our study of the many-body localization (MBL) transition, we integrate the Schrödinger equation exactly by means of a Chebyhsev expansion of the time evolution operator. The dynamics of such systems is probed via a density-density correlation function. Careful analysis of our numerical data gives evidence that the MBL-phase splits into two subphases. In addition to the conceptual relation of the two topics we profit from shared methodology in our kernel polynomial method(KPM) approach in describing these systems.