Correlation-induced metal-insulator transition in the one-dimensional Anderson model

Abstract

We study the nature of the electronic states in tight-binding one-dimensional models with long-range correlated disorder. In particular, we study both diagonal and off-diagonal chains. The energies are considered to be in such a sequency to describe the trace of a fractional Brownian motion with a specified spectral density S( k)∝1/ k α . Using a renormalization group technique, we show that for random on-site energy sequences with anti-persistent increments ( α<2) all energy eigenstates are exponentially localized. On the other hand, for on-site energy sequences with persistent increments ( α>2), the Lyapunov coefficient (inverse localization length) vanishes within a finite range of energy values revealing the presence of an Anderson-like metal–insulator transition. In the case of off-diagonal disorder a phase of delocalized states becomes stable for any α>1.