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Universality in Quantum Hall Systems: Coset Construction of Incompressible States

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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 σH=1/2(e2/h), 1/4(e2/h), 3/5(e2/h), (e2/h),... .

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Authors and Affiliations

  1. Institut für Theoretische Physik, ETH Hönggerberg, CH-8093, Zurich

    Jürg Fröhlich, Bill Pedrini & Johannes Walcher

  2. LPTHE, Université Paris VI, 4 place Jussieu, F-75252, Paris Cedex 05

    Christoph Schweigert

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  1. Jürg Fröhlich
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  2. Bill Pedrini
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  3. Christoph Schweigert
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  4. Johannes Walcher
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Fröhlich, J., Pedrini, B., Schweigert, C. et al. Universality in Quantum Hall Systems: Coset Construction of Incompressible States. Journal of Statistical Physics 103, 527–567 (2001). https://doi.org/10.1023/A:1010389232079

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