---
_id: '7901'
abstract:
- lang: eng
  text: We derive rigorously the leading order of the correlation energy of a Fermi
    gas in a scaling regime of high density and weak interaction. The result verifies
    the prediction of the random-phase approximation. Our proof refines the method
    of collective bosonization in three dimensions. We approximately diagonalize an
    effective Hamiltonian describing approximately bosonic collective excitations
    around the Hartree–Fock state, while showing that gapless and non-collective excitations
    have only a negligible effect on the ground state energy.
acknowledgement: We thank Christian Hainzl for helpful discussions and a referee for
  very careful reading of the paper and many helpful suggestions. NB and RS were supported
  by the European Research Council (ERC) under the European Union’s Horizon 2020 research
  and innovation programme (grant agreement No. 694227). Part of the research of NB
  was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and
  Peter Otte for explanations about the Luttinger model. PTN has received funding
  from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
  Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support
  from the European Research Council (ERC) under the European Union’s Horizon 2020
  research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901).
  BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss
  National Science Foundation through the Grant “Dynamical and energetic properties
  of Bose-Einstein condensates” and from the European Research Council through the
  ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for
  workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz
  Association). NB, PTN, BS, and RS acknowledge support for workshop participation
  from Fondation des Treilles.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
- first_name: Phan Thành
  full_name: Nam, Phan Thành
  last_name: Nam
- first_name: Marcello
  full_name: Porta, Marcello
  last_name: Porta
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy
    of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. 2021;225:885-979.
    doi:<a href="https://doi.org/10.1007/s00222-021-01041-5">10.1007/s00222-021-01041-5</a>
  apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R.
    (2021). Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>.
    Springer. <a href="https://doi.org/10.1007/s00222-021-01041-5">https://doi.org/10.1007/s00222-021-01041-5</a>
  chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
    and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.”
    <i>Inventiones Mathematicae</i>. Springer, 2021. <a href="https://doi.org/10.1007/s00222-021-01041-5">https://doi.org/10.1007/s00222-021-01041-5</a>.
  ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation
    energy of a weakly interacting Fermi gas,” <i>Inventiones Mathematicae</i>, vol.
    225. Springer, pp. 885–979, 2021.
  ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation
    energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.
  mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
    Gas.” <i>Inventiones Mathematicae</i>, vol. 225, Springer, 2021, pp. 885–979,
    doi:<a href="https://doi.org/10.1007/s00222-021-01041-5">10.1007/s00222-021-01041-5</a>.
  short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones
    Mathematicae 225 (2021) 885–979.
date_created: 2020-05-28T16:48:20Z
date_published: 2021-05-03T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00222-021-01041-5
ec_funded: 1
external_id:
  arxiv:
  - '2005.08933'
  isi:
  - '000646573600001'
file:
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  creator: dernst
  date_created: 2022-05-16T12:23:40Z
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has_accepted_license: '1'
intvolume: '       225'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 885-979
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: Inventiones Mathematicae
publication_identifier:
  eissn:
  - 1432-1297
  issn:
  - 0020-9910
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correlation energy of a weakly interacting Fermi gas
tmp:
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  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: 225
year: '2021'
...