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Title: The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus

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.” In this work, it is shown 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.

Authors:
 [1]
  1. Princeton Univ., NJ (United States)
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1512960
Alternate Identifier(s):
OSTI ID: 1464994
Grant/Contract Number:  
SC0002140
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 59; Journal Issue: 8; Journal ID: ISSN 0022-2488
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Haldane, F. D. M. The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus. United States: N. p., 2018. Web. doi:10.1063/1.5046122.
Haldane, F. D. M. The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus. United States. https://doi.org/10.1063/1.5046122
Haldane, F. D. M. 2018. "The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus". United States. https://doi.org/10.1063/1.5046122. https://www.osti.gov/servlets/purl/1512960.
@article{osti_1512960,
title = {The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus},
author = {Haldane, F. D. M.},
abstractNote = {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.” In this work, it is shown 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.},
doi = {10.1063/1.5046122},
url = {https://www.osti.gov/biblio/1512960}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 8,
volume = 59,
place = {United States},
year = {Fri Aug 17 00:00:00 EDT 2018},
month = {Fri Aug 17 00:00:00 EDT 2018}
}

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Cited by: 11 works
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Works referencing / citing this record:

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