Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States

Abstract

We present two novel approaches to establish the local density of states as an order parameter field for the Anderson transition problem. We first demonstrate for 2D quantum Hall systems the validity of conformal scaling relations which are characteristic of order parameter fields. Second we show the equivalence between the critical statistics of eigenvectors of the Hamiltonian and of the transfer matrix, respectively. Based on this equivalence we obtain the order parameter exponent ${\alpha }_0\approx 3.4$ for 3D quantum Hall systems.

4 pages, 3 Postscript figures, corrected scale in Fig.1

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• Point-Contact Conductances from Density Correlations
• Correlation of eigenstates in the critical regime of quantum Hall systems
• Generalized multifractality at spin quantum Hall transition
• Localization in non-chiral network models for two-dimensional disordered wave mechanical systems
• Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder