The Influence of Percolation in the generalized Chalker-Coddington Model

Abstract

We numerically investigate the influence of classical percolation on the quantum Hall localization-delocalization transition. This is accomplished within the framework of the generalized Chalker--Coddington network model which allows us to control the number of {\em classical} saddle points by setting the width $W$ of the saddle point distribution. It is found that increasing this width causes a new microscopic length scale to appear which depends on $W$ and scales with the exponent $X\approx 1.36$ which indicates a close connection to the classical percolation length $\xi$ and its exponent ${\nu }_p=4/3$. Furthermore, the influence of an increase in $W$ on the spectral statistics of the quasienergies of the network model is investigated. An effect similar to the increase of the potential correlation length in the Landau model is seen.

7 pages, 9 figures, 3 tables, submitted to J. Phys. Soc. Jpn

References in corpus (2)

• Spatial and Spectral Multifractality of the Local Density of States at the Mobility Edge
• Spectral Properties of the Chalker-Coddington Network

Cited by in corpus (6)

• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Renormalization group approach to energy level statistics at the integer quantum Hall transition
• Correlated quantum percolation in the lowest Landau level
• Exact spin quantum Hall current between boundaries of a lattice strip
• Modeling Disordered Quantum Systems with Dynamical Networks
• Real-space renormalization-group approach to the integer quantum Hall effect