The problem of Coulomb interactions in the theory of the quantum Hall effect

Abstract

We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkelstein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as Chern-Simons gauge theory. We elaborate on the meaning of a new symmetry ($\mathcal{F}$ invariance) for systems with an infinitely ranged interaction potential. We address the renormalization of the theory and present the main results in terms of a scaling diagram of the conductances.

arXiv comment9 pages, 3 figures. To appear in Proceedings of the International Conference "Mesoscopics and Strongly Correlated Electron Systems", July 2000, Chernogolovka, Russia