Localization properties of disordered chains are calculated using a hierarchy of real-space renormalization techniques, which has previously been applied to the study of densities of states. A systematic study of the energy dependence of the localization lengths and mean-free paths of binary alloys with diagonal and off-diagonal chemical disorder is presented. Results from the renormalization approaches are checked by comparison with results for long chains (${>2\mathrm{}}^{15}$ atoms) calculated using a related decimation technique with no configuration averaging. The effect of short-range order is explored and a scaling relation for the increase of localization lengths with short-range order is described. For purely-off-diagonal disorder, the localization length of the state at the center of the spectrum is found to be infinite, in agreement with previous exact results. For a specific type of chemical off-diagonal disorder we show that this state is strictly delocalized. There is no fluctuation-induced localization with exp(-λ’ √L ) decay like that found for other types of disorder such as structural disorder. The renormalization techniques can also treat chains with continuous distributions of disorder, and reproduce the exact localization lengths for the Lloyd model.

• Received 10 June 1985

DOI:https://doi.org/10.1103/PhysRevB.32.4576