Delocalization in the 1D Anderson Model with Long-Range Correlated Disorder

Abstract

We study the nature of electronic states in a tight-binding one-dimensional model with the on-site energies exhibiting long-range correlated disorder and nonrandom hopping amplitudes. The site energies describe the trace of a fractional Brownian motion with a specified spectral density $S\left(k\right)\propto 1/k^{\alpha }$. Using a renormalization group technique, we show that for long-range correlated energy sequences with persistent increments ( $\alpha >2\mathrm{}$) the Lyapunov coefficient (inverse localization length) vanishes within a finite range of energy values revealing the presence of an Anderson-like metal-insulator transition.