### 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.

Original language | English (US) |
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Pages (from-to) | 503-535 |

Number of pages | 33 |

Journal | Communications In Mathematical Physics |

Volume | 285 |

Issue number | 2 |

DOIs | |

State | Published - Jan 2009 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Jansen, S., Lieb, E. H., & Seiler, R. (2009). Symmetry breaking in Laughlin's state on a cylinder.

*Communications In Mathematical Physics*,*285*(2), 503-535. https://doi.org/10.1007/s00220-008-0576-4