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

TL;DR

This paper investigates how long-range correlated disorder affects the metal-insulator transition in a 1D tight-binding model, revealing the role of disorder strength and correlation in localization and mobility edges.

Contribution

It provides a detailed analysis of the impact of power-law correlated disorder on localization, identifying the conditions for extended states and deriving the critical exponent for localization length.

Findings

Extended eigenstates exist for >2 with mobility edges at =|2-W/2|

Critical exponent =1+1.4e^{2-} depends on correlation degree 

Disorder strength W determines mobility edges, correlation  influences critical exponents

Abstract

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 $[-\frac{W}{2},\frac{W}{2}]$ and having a power-law spectral density $S(k)\propto k^{-\alpha}$, 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 $\alpha>2$, and the mobility edges are at $\pm E_{c}=\pm|2-W/2|$. Furthermore, we find the critical exponent $\nu$ of localization length ($\xi \sim |E-E_{c}|^{-\nu}$) to be $\nu=1+1.4e^{2-\alpha}$. Thus our results indicate that the disorder strength $W$ determines the mobility edges and the degree of correlation $\alpha$ determines the critical exponents.