---
_id: '10600'
abstract:
- lang: eng
  text: We show that recent results on adiabatic theory for interacting gapped many-body
    systems on finite lattices remain valid in the thermodynamic limit. More precisely,
    we prove a generalized super-adiabatic theorem for the automorphism group describing
    the infinite volume dynamics on the quasi-local algebra of observables. The key
    assumption is the existence of a sequence of gapped finite volume Hamiltonians,
    which generates the same infinite volume dynamics in the thermodynamic limit.
    Our adiabatic theorem also holds for certain perturbations of gapped ground states
    that close the spectral gap (so it is also an adiabatic theorem for resonances
    and, in this sense, “generalized”), and it provides an adiabatic approximation
    to all orders in the adiabatic parameter (a property often called “super-adiabatic”).
    In addition to the existing results for finite lattices, we also perform a resummation
    of the adiabatic expansion and allow for observables that are not strictly local.
    Finally, as an application, we prove the validity of linear and higher order response
    theory for our class of perturbations for infinite systems. While we consider
    the result and its proof as new and interesting in itself, we also lay the foundation
    for the proof of an adiabatic theorem for systems with a gap only in the bulk,
    which will be presented in a follow-up article.
acknowledgement: J.H. acknowledges partial financial support from ERC Advanced Grant
  “RMTBeyond” No. 101020331.
article_number: '011901'
article_processing_charge: No
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 uniform gap. <i>Journal of Mathematical Physics</i>. 2022;63(1). doi:<a
    href="https://doi.org/10.1063/5.0051632">10.1063/5.0051632</a>'
  apa: 'Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic
    limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. AIP
    Publishing. <a href="https://doi.org/10.1063/5.0051632">https://doi.org/10.1063/5.0051632</a>'
  chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
    Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>. AIP
    Publishing, 2022. <a href="https://doi.org/10.1063/5.0051632">https://doi.org/10.1063/5.0051632</a>.'
  ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
    Systems with a uniform gap,” <i>Journal of Mathematical Physics</i>, vol. 63,
    no. 1. AIP Publishing, 2022.'
  ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
    Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.'
  mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
    Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>, vol.
    63, no. 1, 011901, AIP Publishing, 2022, doi:<a href="https://doi.org/10.1063/5.0051632">10.1063/5.0051632</a>.'
  short: S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).
date_created: 2022-01-03T12:19:48Z
date_published: 2022-01-03T00:00:00Z
date_updated: 2025-04-14T07:57:17Z
day: '03'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1063/5.0051632
ec_funded: 1
external_id:
  arxiv:
  - '2012.15238'
  isi:
  - '000739446000009'
intvolume: '        63'
isi: 1
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2012.15238
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
  eissn:
  - 1089-7658
  issn:
  - 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...