5,847 research outputs found
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
( 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 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.
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