Level statistics for quantum Hall systems

Abstract

Level statistics for two classes of disordered systems at criticality are analyzed in terms of different realizations of the Chalker–Coddington network model. These include: 1) Re-examination of the standard U(1) model describing dynamics of electrons on the lowest Landau level in the quantum Hall effect, where it is shown that after proper local unfolding the nearest-neighbor spacing distribution (NNSD) at the critical energy follows the Wigner surmise for Gaussian unitary ensembles (GUE). 2) Quasi-particles in disordered superconductors with broken time reversal and spin rotation invariance (in the language of random matrix theory this system is a representative of symmetry class D in the classification scheme of Altland and Zirnbauer). Here again the NNSD obeys the Wigner surmise for GUE, reflecting therefore only «basic» discrete symmetries of the system (time reversal violation) and ignoring particle–hole symmetries and other finer details (criticality). In the localized regime level repulsion is suppressed.