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

TL;DR

This paper introduces two new methods to analyze the local density of states as an order parameter in Anderson transitions, demonstrating conformal scaling and eigenvector statistics equivalence in quantum Hall systems.

Contribution

It presents novel approaches linking local density of states to order parameter fields and establishes the equivalence of eigenvector statistics, providing new insights into quantum Hall transitions.

Findings

Conformal scaling relations validated for 2D quantum Hall systems

Equivalence between eigenvector statistics of Hamiltonian and transfer matrix

Estimated order parameter exponent α₀ ≈ 3.4 for 3D quantum Hall systems

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.