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The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in…
After Anderson's prediction of disorder-induced insulating behavior, extensive work found no singularities in the density of states of localized systems. However, Johri and Bhatt recently uncovered the existence of a non-analyticity in the…
Controlling the magnetic properties of nanosystems by an electric field offers a number of advantages for spintronics applications. Using the noncollinear Alexander-Anderson model, we have shown that the interaction of localized magnetic…
Anderson localization was discovered 50 years ago to describe the propagation of electrons in the presence of disorder. The main prediction back then, was the existence of disorder induced localized states, which do not conduct electricity.…
Localization of wavefunctions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [[V. Khemani, R. Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary to naive…
Electron localization property of a random chain changing under the influence of a constant electric field has been studied. We have adopted the multifractal scaling formalism to explore the possible localization behavior in the system. We…
Using the fractional moment method it is shown that, within the Hartree-Fock approximation for the Disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential…
We study the two-dimensional paramagnetic Anderson-Hubbard model using an extension of dynamical mean-field theory that allows us to treat disorder and strong electronic correlations on equal footing. We investigate the scaling of the…
We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of…
We study electron localization in disordered quantum systems, focusing on both individual eigenstates and thermal states. We employ complex polarization as a numerical indicator to characterize the system's localization length. Furthermore,…
We have completed a numerical investigation of the Anderson-Hubbard model for three-dimensional simple cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation…
We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. By using an efficient numerical method which is based on exact diagonalization in a truncated basis of…
The interplay between local, repulsive interactions and disorder acting only on one spin orientation of lattice fermions ("spin-dependent disorder") is investigated. The nonmagnetic disorder vs. interaction phase diagram is computed using…
We study analytically and numerically the problem of two particles with a long range attractive interaction on a two-dimensional (2d) lattice with disorder. It is shown that below some critical disorder the interaction creates delocalized…
We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model,…
The impact of a weak electric field on the weak-localization corrections is studied within the framework of a nonlinear sigma-model. Two scaling regimes are obtained. In one, the scaling is dominated by temperature; in the other, by the…
We study the effect of electron-electron interaction on a two dimensional (2D) disordered lattice. For the case of two electrons the analytical estimates are presented showing a transition from localized to delocalized states in a way…
The effects of dynamic localization in a solid-state system -- a quantum dot -- are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent…
We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range…
Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this…