Related papers: Universality in Anderson localization on random gr…
We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in…
Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
We consider a chain of interacting fermions with random disorder that was intensively studied in the context of many-body localization. We show that only a small fraction of the two-body interaction represents a true local perturbation to…
We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…
We undertake an exact numerical study of the effects of disorder on the Anderson localization of electronic states in graphene. Analyzing the scaling behaviors of inverse participation ratio and geometrically averaged density of states, we…
We demonstrate the level statistics in the vicinity of the Anderson transition in $d>2$ dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of…
We examine the interplay between disorder and fractionality in a one-dimensional tight-binding Anderson model. In the absence of disorder, we observe that the two lowest energy eigenvalues detach themselves from the bottom of the band, as…
We present two complementary simulations that lead to an exploration of Anderson localization, a phenomenon in which wave diffusion is suppressed in disordered media by interference from multiple scattering. To build intuition, the first…
We study the nonequilibrium properties of a nonergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. The ground state and excited states of this…
We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the…
We consider Hermitian and symmetric random band matrices on the $d$-dimensional lattice $(\mathbb{Z}/L\mathbb{Z})^d$ with bandwidth $W$, focusing on local eigenvalue statistics at the spectral edge in the limit $W\to\infty$. Our analysis…
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model, the Anderson-Edwards model. Using the density-matrix renormalization group…
We generalize universal relations between the multifractal exponent \alpha_0 for the scaling of the typical wave function magnitude at a (Anderson) localization-delocalization transition in two dimensions and the corresponding critical…
Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the $\beta$-ensemble, known for its structural simplicity.…
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…
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…
By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length of the adjacency matrices of Erd\H{o}s-R\'enyi (ER) {\it fully}…
The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A…
Anderson localization problem for non-interacting two-dimensional electron gas subject to strong magnetic field, disordered potential and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding…