INTEGER QUANTUM HALL-EFFECT FOR LATTICE FERMIONS

A two-dimensional lattice model for non-interacting fermions in a magn etic field with half a flux quantum per plaquette and N levels per sit e is considered. This is a model which exhibits the integer quantum Ha ll effect (IQHE) in the presence of disorder. It presents an alternati ve to the continuous picture for the IQHE with Landau levels. The larg e-N limit can be solved: two Hall transitions appear and there is an i nterpolating behaviour between the two Hall plateaux. Although this ap proach to the IQHE is different from the traditional one with Landau l evels because of different symmetries (continuous for Landau levels an d discrete here), some characteristic features are reproduced. For ins tance, the slope of the Hall conductivity is infinite at the transitio n points and the electronic states are delocalized only at the transit ions.