Related papers: Advanced Lanczos diagonalization for models of qua…
We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable…
Random scattering of photons in disordered one-dimensional solids gives rise to an exponential suppression of transmission, which is known as Anderson localization. Here, we experimentally study Anderson localization in a superconducting…
A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the…
We show that the tails of the asymptotic density distribution of a quantum wave packet that localizes in the the presence of random or quasiperiodic disorder can be described by the diagonal term of the projection over the eingenstates of…
We suggest that low-lying eigenvalues of realistic quantum many-body hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated, instead of the full diagonalization, by the diagonalization of small truncated…
The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two non-perturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and…
We report a study of a disorder-dependent real-space representation of the quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can…
We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a…
The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the…
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…
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…
The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from…
Anderson localization is a fundamental phenomenon in disordered quantum systems, where transport is suppressed by wave interference from extensive randomness. Moving beyond traditional multi-impurity scenarios, we investigate…
We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electrons or excitons in crystals with short-range particle-lattice interactions. Applying a very…
Manipulating energy levels while controlling the electron localization is an essential step for many applications of confined systems. In this paper we demonstrate how to achieve electron localization and induce energy level oscillation in…
We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
We investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of…
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the…
We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical…