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

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.

6 pages, 6 figures

References in corpus (5)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition
• Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices
• AC-field-controlled localization-delocalization transition in one dimensional disordered system

Cited by in corpus (1)

• Bound states in one-dimensional systems with colored noise