---
_id: '8091'
abstract:
- lang: eng
text: In the setting of the fractional quantum Hall effect we study the effects
of strong, repulsive two-body interaction potentials of short range. We prove
that Haldane’s pseudo-potential operators, including their pre-factors, emerge
as mathematically rigorous limits of such interactions when the range of the potential
tends to zero while its strength tends to infinity. In a common approach the interaction
potential is expanded in angular momentum eigenstates in the lowest Landau level,
which amounts to taking the pre-factors to be the moments of the potential. Such
a procedure is not appropriate for very strong interactions, however, in particular
not in the case of hard spheres. We derive the formulas valid in the short-range
case, which involve the scattering lengths of the interaction potential in different
angular momentum channels rather than its moments. Our results hold for bosons
and fermions alike and generalize previous results in [6], which apply to bosons
in the lowest angular momentum channel. Our main theorem asserts the convergence
in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after
appropriate energy scalings, to Hamiltonians with contact interactions in the
lowest Landau level.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\nThe work of R.S. was supported by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC
Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. "
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 2020;181:448-464.
doi:10.1007/s10955-020-02586-0
apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials
in systems with short-range interactions. Journal of Statistical Physics.
Springer. https://doi.org/10.1007/s10955-020-02586-0
chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics.
Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0.
ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems
with short-range interactions,” Journal of Statistical Physics, vol. 181.
Springer, pp. 448–464, 2020.
ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems
with short-range interactions. Journal of Statistical Physics. 181, 448–464.
mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials
in Systems with Short-Range Interactions.” Journal of Statistical Physics,
vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0.
short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.
date_created: 2020-07-05T22:00:46Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T07:51:47Z
day: '01'
ddc:
- '530'
department:
- _id: RoSe
doi: 10.1007/s10955-020-02586-0
ec_funded: 1
external_id:
arxiv:
- '2001.07144'
isi:
- '000543030000002'
file:
- access_level: open_access
checksum: 5cbeef52caf18d0d952f17fed7b5545a
content_type: application/pdf
creator: dernst
date_created: 2020-11-25T15:05:04Z
date_updated: 2020-11-25T15:05:04Z
file_id: '8812'
file_name: 2020_JourStatPhysics_Seiringer.pdf
file_size: 404778
relation: main_file
success: 1
file_date_updated: 2020-11-25T15:05:04Z
has_accepted_license: '1'
intvolume: ' 181'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 448-464
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- '15729613'
issn:
- '00224715'
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Emergence of Haldane pseudo-potentials in systems with short-range interactions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 181
year: '2020'
...