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:
-
- 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}
}
Web of Science
Works referenced in this record:
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Works referencing / citing this record:
Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
journal, January 2020
- Rückert, Janna E.; Roósz, Gergő; Timm, Carsten
- Physical Review B, Vol. 101, Issue 2
Dirac Fermion Hierarchy of Composite Fermi Liquids
journal, June 2019
- Wang, Jie
- Physical Review Letters, Vol. 122, Issue 25
Lattice Monte Carlo for Quantum Hall States on a Torus
text, January 2017
- Wang, Jie; Geraedts, Scott D.; Rezayi, E. H.
- arXiv