The Edge State Network Model and the Global Phase Diagram

Abstract

The effects of randomness are investigated in the fractional quantum Hall systems. Based on the Chern-Simons Ginzburg-Landau theory and considering relevant quasi-particle tunneling, the edge state network model for the hierarchical state is introduced and the plateau-plateau transition and the liquid-insulator transition are discussed. This model has duality which corresponds to the relation of the quantum Hall liquid phase and the Hall insulating phase and reveals a mechanism of plateau transition in the weak coupling regime.