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

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 ($\cal F$ 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.Comment: 9 pages, 3 figures. To appear in Proceedings of the International Conference "Mesoscopics and Strongly Correlated Electron Systems", July 2000, Chernogolovka, Russi

Fractional Quantum Hall States in Ultracold Rapidly Rotating Dipolar Fermi Gases

We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultra-cold two dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction $\nu =1/3$ is well-described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow to realize these very interesting highly correlated states in future experiments.Comment: 4 pages, 2 figure

(Mis-)handling gauge invariance in the theory of the quantum Hall effect II: Perturbative results

The concept of F-invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2\epsilon spatial dimensions. We report the results of a detailed renormalization group analysis and establish the renormalizability of the (Finkelstein) action to two loop order. We show that the infrared behavior of the theory can be extracted from gauge invariant (F-invariant) quantities only. For these quantities (conductivity, specific heat) we derive explicit scaling functions. We identify a bosonic quasiparticle density of states which develops a Coulomb gap as one approaches the metal-insulator transition from the metallic side. We discuss the consequences of F-invariance for the strong coupling, insulating regime.Comment: 26 pages, 7 figures; minor modifications; submitted to Phys.Rev.

(Mis-)handling gauge invariance in the theory of the quantum Hall effect I: Unifying action and the \nu=1/2 state

We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and Chern-Simons gauge theory. We elaborate on the microscopic origins of the effective action and unravel a new symmetry in the problem with Coulomb interactions which we name F-invariance. This symmetry has a broad range of physical consequences which will be the main topic of future analyses. In the second half of this paper we compute the response of the theory to electromagnetic perturbations at a tree level approximation. This is applicable to the theory of ordinary metals as well as the composite fermion approach to the half-integer effect. Fluctuations in the Chern-Simons gauge fields are found to be well behaved only when the theory is F-invariant.Comment: 20 pages, 6 figures; appendix B revised; submitted to Phys.Rev.