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

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, χ0ex0ex=0ex0exη/2d, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of a unitary network model and represent a new method to investigate spectral properties of disordered systems.