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It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…

We study the effect of strong correlations on the zero bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model, which has both on-site and nearest-neighbor interactions on a…

We report on the impact of variable-scale disorder on 3D Anderson localization of a non-interacting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a…

We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of…

The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of…

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at…

We analyze the complex interplay of the strong correlations and impurities in a high temperature superconductor and show that both the nature and degree of the inhomogeneities at zero temperature in the local order parameters change…

We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can…

I study the quasiparticle level correlations in a grain of a weakly disordered d-wave superconductor, and show that, in a wide intermediate energy range, they are characterized by a novel type of universal behavior.

Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a…

We study the disordered Heisenberg spin chain, which exhibits many body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational…

For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…

Recently it has been shown that transmon qubit architectures experience a transition between a many-body localized and a quantum chaotic phase. While it is crucial for quantum computation that the system remains in the localized regime, the…

We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant…

The Anderson transition of Bogoliubov-de Gennes (BdG) quasiparticles in superconducting state has been studied theoretically for last three decades. However, its experimental proof is lacking. In particular, the relationship of the…

We study Anderson localization in disordered helical conductors that are obtained from one-dimensional conductors with spin-orbit interaction and a magnetic field, or from equivalent systems. We call such conductors "quasi-helical" because…

A consequence of the disorder and Coulomb interaction competition is the electron-glass phase observed in several Anderson-insulators. The disorder in these systems, typically degenerate semiconductors, is stronger than the interaction,…

We have computed persistent currents in a disordered mesoscopic ring in the presence of small electron-electron interactions, treated in first order perturbation theory. We have investigated both a contact (Hubbard) and a nearest neighbour…

We present a general theory of the superconductive proximity effect in disordered normal--superconducting (N-S) structures, based on the recently developed Keldysh action approach. In the case of the absence of interaction in the normal…

We analyze the effect of the non-vanishing range of electron-electron repulsion on the mechanism of unconventional superconductivity. We present asymptotically exact weak-coupling results for dilute electrons in the continuum and for the 2D…