Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect

Abstract

We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.

6 pages REVTeX, 9 postscript figures and 1 postscript table

References in corpus (5)

• Random-Matrix Theory of Quantum Transport
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Conductance fluctuations at the integer quantum Hall plateau transition
• Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach
• Real Space Renormalization of the Chalker-Coddington Model

Cited by in corpus (5)

• Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
• Renormalization group approach to energy level statistics at the integer quantum Hall transition
• Fluctuating Hall resistance defeats the quantized Hall insulator
• Localization in non-chiral network models for two-dimensional disordered wave mechanical systems
• Real-space renormalization-group approach to the integer quantum Hall effect