Beyond the universal Dyson singularity for 1-D chains with hopping disorder
Abstract
We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain - that of random walks and diffusion with anomalous exponents.
Cite
@article{arxiv.2107.08518,
title = {Beyond the universal Dyson singularity for 1-D chains with hopping disorder},
author = {Akshay Krishna and R. N. Bhatt},
journal= {arXiv preprint arXiv:2107.08518},
year = {2021}
}
Comments
This is the preprint of an article that has been accepted to a forthcoming Special Issue of the Annals of Physics. The Special Issue will contain Proceedings of the Localisation 2020 conference and is dedicated to Philip W. Anderson. The DOI links to the final version in press