---
_id: '10643'
abstract:
- lang: eng
  text: "We prove a generalised super-adiabatic theorem for extended fermionic systems
    assuming a spectral gap only in the bulk. More precisely, we assume that the infinite
    system has a unique ground state and that the corresponding Gelfand–Naimark–Segal
    Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that
    a similar adiabatic theorem also holds in the bulk of finite systems up to errors
    that vanish faster than any inverse power of the system size, although the corresponding
    finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"
acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant
  ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft
  and the Open Access Publishing Fund of the University of Tübingen is gratefully
  acknowledged.
article_number: e4
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Stefan
  full_name: Teufel, Stefan
  last_name: Teufel
citation:
  ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
    with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href="https://doi.org/10.1017/fms.2021.80">10.1017/fms.2021.80</a>'
  apa: 'Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic
    limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/fms.2021.80">https://doi.org/10.1017/fms.2021.80</a>'
  chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
    Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge
    University Press, 2022. <a href="https://doi.org/10.1017/fms.2021.80">https://doi.org/10.1017/fms.2021.80</a>.'
  ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
    Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10.
    Cambridge University Press, 2022.'
  ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
    Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.'
  mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
    Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol.
    10, e4, Cambridge University Press, 2022, doi:<a href="https://doi.org/10.1017/fms.2021.80">10.1017/fms.2021.80</a>.'
  short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).
corr_author: '1'
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2025-04-14T07:57:17Z
day: '18'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1017/fms.2021.80
ec_funded: 1
external_id:
  arxiv:
  - '2012.15239'
  isi:
  - '000743615000001'
file:
- access_level: open_access
  checksum: 87592a755adcef22ea590a99dc728dd3
  content_type: application/pdf
  creator: cchlebak
  date_created: 2022-01-19T09:27:43Z
  date_updated: 2022-01-19T09:27:43Z
  file_id: '10646'
  file_name: 2022_ForumMathSigma_Henheik.pdf
  file_size: 705323
  relation: main_file
  success: 1
file_date_updated: 2022-01-19T09:27:43Z
has_accepted_license: '1'
intvolume: '        10'
isi: 1
keyword:
- computational mathematics
- discrete mathematics and combinatorics
- geometry and topology
- mathematical physics
- statistics and probability
- algebra and number theory
- theoretical computer science
- analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
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: 10
year: '2022'
...