Critical parameters for the one-dimensional systems with long-range correlated disorder

We study the metal–insulator transition in a tight-binding one-dimensional (1D) model with long-range correlated disorder. In the case of diagonal disorder with site energy within [−W/2,W/2][−W/2,W/2] and having a power-law spectral density S(k)∝k−αS(k)∝k−α, we investigate the competition between the disorder and correlation. Using the transfer-matrix method and finite-size scaling analysis, we find out that there is a finite range of extended eigenstates for α>2α>2, and the mobility edges are at ±Ec=±|2−W/2|±Ec=±|2−W/2|. Furthermore, we find the critical exponent νν of localization length (ξ∼|E−Ec|−νξ∼|E−Ec|−ν) to be ν=1+1.4e2−αν=1+1.4e2−α. Thus our results indicate that the disorder strength W   determines the mobility edges and the degree of correlation αα determines the critical exponents.