Related papers: Anderson mobility edge as a percolation transition
The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich of counter-intuitive…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
It is shown that the Coulomb interaction can lead to delocalization of two electron states in two-dimensional (2D) disordered potential in a way similar to the Anderson transition in three dimensions (3D). At fixed disorder strength the…
A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to…
We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By…
As disorder strength increases in quantum many-body systems a new phase of matter, the so-called anybody localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that…
In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…
Motivated by experimental progress in cold atomic systems, we use and advance Localisation Landscape Theory (LLT), to examine two-dimensional systems with point-like random scatterers. We begin by showing that exact eigenstates cannot be…
In this Letter we study numerically the Anderson model on partially disordered random regular graphs (RRG) considered as the toy model for a Hilbert space of interacting disordered many-body system. The protected subsector of zero-energy…
The three-dimensional Anderson model is a well-studied model of disordered electron systems that shows the delocalization--localization transition. As in our previous papers on two- and three-dimensional (2D, 3D) quantum phase transitions…
Anderson localization is fundamentally controlled by dimensionality, yet the nature of the Anderson transition in continuously tunable noninteger dimensions remains largely unexplored. Here, we introduce a family of three-dimensional…
We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe…
For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…
We show that in the one-dimensional (1D) Anderson model long-range correlations within the sequence of on-site potentials may lead to a region of extended states in the vicinity of the band centre, i.e., to a correlation-induced…
Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly…
This work establishes the Anderson localization in both the spectral exponential and the strong dynamical localization for the multi-particle Anderson tight-binding model with correlated but strongly mixing random external potential. The…
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…
This study is concerned with destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schr\"odinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically…