Lowest Landau level broadened by a Gaussian random potential with an arbitrary correlation length: An efficient continued-fraction approach

TL;DR

This paper develops an efficient continued-fraction method to approximate the averaged density of states for electrons in a magnetic field with a Gaussian random potential, extending Wegner's exact result to finite correlation lengths.

Contribution

It introduces a novel continued-fraction extrapolation technique to handle finite correlation lengths in the lowest Landau level broadening problem.

Findings

Successfully extended Wegner's result to non-zero correlation length

Achieved reliable approximation of the density of states

Demonstrated the effectiveness of the continued-fraction approach

Abstract

For an electron in the plane subjected to a perpendicular constant magnetic field and a homogeneous Gaussian random potential with a Gau{ss}ian covariance function we approximate the averaged density of states restricted to the lowest Landau level. To this end, we extrapolate the first 9 coefficients of the underlying continued fraction consistently with the coefficients' high-order asymptotics. We thus achieve the first reliable extension of Wegner's exact result [Z. Phys. B {\bf 51}, 279 (1983)] for the delta-correlated case to the physically more relevant case of a non-zero correlation length.