Integer Quantum Hall Effect for Lattice Fermions

TL;DR

This paper introduces a lattice model for non-interacting fermions in a magnetic field that exhibits the Integer Quantum Hall Effect, providing an alternative to Landau level-based models and analyzing phase transitions and state localization.

Contribution

It presents a solvable lattice model for IQHE with disorder, demonstrating Hall transitions and delocalized states, differing from traditional Landau level approaches.

Findings

Two Hall transitions observed in the large N limit

Delocalized states only at transition points

Infinite slope of Hall conductivity at transitions

Abstract

A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the presence of disorder. It presents an alternative to the continuous picture for the IQHE with Landau levels. The large $N$ limit can be solved: two Hall transitions appear and there is an interpolating behavior between the two Hall plateaux. Although this approach to the IQHE is different from the traditional one with Landau levels because of different symmetries (continuous for Landau levels and discrete here), some characteristic features are reproduced. For instance, the slope of the Hall conductivity is infinite at the transition points and the electronic states are delocalized only at the transitions.