### Abstract

Holomorphic functions that characterize states in a two-dimensional Landau level have been central to key developments such as the Laughlin state. Their origin has historically been attributed to a special property of “Schrödinger wavefunctions” of states in the “lowest Landau level.” It is shown here that they instead arise in any Landau level as a generic mathematical property of the Heisenberg description of the non-commutative geometry of guiding centers. When quasiperiodic boundary conditions are applied to compactify the system on a torus, a new formula for the overlap between holomorphic states, in the form of a discrete sum rather than an integral, is obtained. The new formula is unexpected from the previous “lowest-Landau level Schrödinger wavefunction” interpretation.

Original language | English (US) |
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Article number | 081901 |

Journal | Journal of Mathematical Physics |

Volume | 59 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2018 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics