Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

Abstract

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $η$ and the spectral compressibility $χ$ at the mobility edge, $χ=η/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.