Universality in Quantum Hall Systems: Coset Construction of Incompressible States

Abstract

Incompressible Quantum Hall fluids (QHF's) can be described in the scaling limit by three-dimensional topological field theories. Thanks to the correspondence between three-dimensional topological field theories and two dimensional chiral conformal field theories (CCFT's), we propose to study QHF's from the point of view of CCFT's. We derive consistency conditions and stability criteria for those CCFT's that can be expected to describe a QHF. A general algorithm is presented which uses simple currents to construct interesting examples of such CCFT's. It generalizes the description of QHF's in terms of Quantum Hall lattices. Explicit examples, based on the coset construction, provide candidates for the description of Quantum Hall fluids with Hall conductivity s_H=1/2 e^2/h, 1/4 e^2/h, 3/5 e^2/h, e^2/h,...

arXiv comment36 pages, LaTeX2e, AMSLaTeX; dedicated to the memory of Quin Luttinger. References added, typos fixed

References in corpus (7)

• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• Edge excitations of paired fractional quantum Hall states
• TASI lectures on the Holographic Principle
• The resolution of field identification fixed points in diagonal coset theories
• Logarithmic Conformal Field Theory and Seiberg-Witten Models
• On edge states in semi-infinite quantum Hall systems
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Cited by in corpus (13)

• TFT construction of RCFT correlators III: Simple currents
• Parafermion Hall states from coset projections of abelian conformal theories
• Twenty-five years of two-dimensional rational conformal field theory
• Physical principles underlying the quantum Hall effect
• Conformal field theory, boundary conditions and applications to string theory
• Scaling dimension of quantum Hall quasiparticles from tunneling current noise measurements
• Paired states on a torus
• The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics
• Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands
• New maverick coset theories
• Stability and Activation Gaps of Parafermionic Hall States in the Second Landau Level
• Braiding properties of paired spin-singlet and non-abelian hierarchy states
• Two-dimensional conformal field theory and beyond. Lessons from a continuing fashion