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Symmetry Breaking in Laughlin’s State on a Cylinder

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Abstract

We investigate Laughlin’s fractional quantum Hall effect wave function on a cylinder. We show that it displays translational symmetry breaking in the axial direction for sufficiently thin cylinders. At filling factor 1/p, the period is p times the period of the filled lowest Landau level. The proof uses a connection with one-dimensional polymer systems and discrete renewal equations.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany

    S. Jansen & R. Seiler

  2. Department of Mathematics, Princeton University, P. O. Box 708, Princeton, NJ, 08544, USA

    E. H. Lieb

Authors
  1. S. Jansen
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  2. E. H. Lieb
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  3. R. Seiler
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Correspondence to S. Jansen.

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Communicated by H. Spohn

© 2008 by the Authors. This paper may be reproduced, in its entirety, for non-commercial purposes.

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Jansen, S., Lieb, E.H. & Seiler, R. Symmetry Breaking in Laughlin’s State on a Cylinder. Commun. Math. Phys. 285, 503–535 (2009). https://doi.org/10.1007/s00220-008-0576-4

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  • DOI: https://doi.org/10.1007/s00220-008-0576-4

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