Related papers: Anderson localization transition in disordered hyp…
It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be…
Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce…
We investigate a celebrated problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization from a novel perspective. A binary disorder is assumed to be created by immobile heavy particles for the…
One of the daunting challenges in optical physics is to accurately control the flow of light at the subwavelength scale, by patterning the optical medium one can design anisotropic media. The light transport can also be significantly…
We study the Anderson transition for three-dimensional (3D) $N \times N \times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and…
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal…
We theoretically investigate light propagation and Anderson localization in one-dimensional disordered superlattices composed of dielectric stacks with graphene sheets in between. Disorder is introduced either on graphene material…
Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques…
We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of…
Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition a reliable extraction of…
We investigate the formation of bound states made of two interacting atoms moving in a one dimensional (1D) quasi-periodic optical lattice. We derive the quantum phase diagram for Anderson localization of both attractively and repulsively…
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…
Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context…
We reinvestigate the behavior of the conductivity of several disordered quantum lattice models at infinite temperature using exact diagonalization. Contrary to the conclusion drawn in a recent investigation of similar quantities in…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution…
Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson…
This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the…
The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for…
We study quantum phase transitions of three-dimensional disordered systems in the chiral classes (AIII and BDI) with and without weak topological indices. We show that the systems with a nontrivial weak topological index universally exhibit…