Related papers: Static Screening and Delocalization Effects in the…
I discuss the properties of electron states in amorphous Si based on large scale calculations with realistic several thousand atom models. A relatively simple model for the localized to extended (Anderson) transition is reviewed. Then, the…
We consider a Periodic Anderson Model (PAM) with a momentum-dependent inter-band hybridization that is strongly suppressed near the Fermi level. Under these conditions, we reduce the PAM to an effective low-energy Hamiltonian, $H_{\rm…
In models of hopping disorder in the absence of external fields and at the band center, the electrons are less localized in space than the standard exponential Anderson localization. A signature of this anomalous localization is the square…
We use the inverse participation ratio based on the Husimi function to perform a phase space analysis of the Anderson model in one, two, and three dimensions. Important features of the quantum states remain observable in phase space in the…
We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and {\it non-random} long-range inter-site interaction $J_{mn}=J/|m-n|^{\mu}$. The model is critical at $1<\mu<3/2$ and reveals the…
The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper…
We numerically investigate how electron-electron interactions influence the transport properties of disordered electrons in two dimensions. Our study is based on the quantum Coulomb glass model appropriately generalized to include the spin…
We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i -…
We use the regularized kernel polynomial method (RKPM) to numerically study the effect disorder on a single layer of graphene. This accurate numerical method enables us to study very large lattices with millions of sites, and hence is…
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…
We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $\ell$ as a power-law $1/\ell^\alpha$. Using a combination of…
We develop a non-perturbative numerical method to study tunneling of a single electron through an Aharonov-Bohm ring where several strongly interacting electrons are bound. Inelastic processes and spin-flip scattering are taken into…
We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagom\'e, the square, and the…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
We show the localization transition and its effect on two dynamical processes for an extended Aubry-Andr\'e-Harper model with incommensurate on-site and hopping potentials. After specifying an extended Aubry-Andr\'e-Harper model, we check…
The Hubbard model on a semi-infinite three-dimensional lattice is considered to investigate electron-correlation effects at single-crystal surfaces. The standard second-order perturbation theory in the interaction U is used to calculate the…
Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson localization. Although we have well established…
We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice…