Fluctuations of electron energy levels in the interger quantum hall effect

Abstract

The level statistics in the regime of the quantum Hall effect is studied. The critical exponent of the localization length is found by analyzing the lowest Landau band. By scaling procedure for different system sizes we find the spectral compressability at the plateau-plateau transition. It turned out to be scale-invariant. Obtained results are generalized for other special dimensionalities. Our findings are characteristic of the critical unitary class of universality. For two-dimensional systems the tail of the level spacing distribution resembles the Poisson distribution. It is similar to that of three-dimensional systems, although the exponential rate is as twice as large. Fluctuations of the energy levels are distinct from the classical Gaussian unitary ensemble data and reflect the multifractal nature of the electron wave functions