---
_id: '10642'
abstract:
- lang: eng
  text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized
    but otherwise arbitrary perturbations of weakly interacting quantum spin systems
    with uniformly gapped on-site terms change the ground state of such a system only
    locally, even if they close the spectral gap. We call this a strong version of
    the local perturbations perturb locally (LPPL) principle which is known to hold
    for much more general gapped systems, but only for perturbations that do not close
    the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle
    to Hamiltonians that have the appropriate structure of gapped on-site terms and
    weak interactions only locally in some region of space. While our results are
    technically corollaries to a theorem of Yarotsky, we expect that the paradigm
    of systems with a locally gapped ground state that is completely insensitive to
    the form of the Hamiltonian elsewhere extends to other situations and has important
    physical consequences.
acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced
  Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for
  very helpful comments and discussions and Jürg Fröhlich for references to the literature.
  Open Access funding enabled and organized by Projekt DEAL.
article_number: '9'
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
- first_name: Tom
  full_name: Wessel, Tom
  last_name: Wessel
citation:
  ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally
    gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical
    Physics</i>. 2022;112(1). doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>
  apa: Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground
    states in locally gapped and weakly interacting quantum spin systems. <i>Letters
    in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>
  chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of
    Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.”
    <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>.
  ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states
    in locally gapped and weakly interacting quantum spin systems,” <i>Letters in
    Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022.
  ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in
    locally gapped and weakly interacting quantum spin systems. Letters in Mathematical
    Physics. 112(1), 9.
  mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped
    and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>,
    vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>.
  short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).
date_created: 2022-01-18T16:18:25Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11005-021-01494-y
ec_funded: 1
external_id:
  arxiv:
  - '2106.13780'
  isi:
  - '000744930400001'
  pmid:
  - '35125630'
file:
- access_level: open_access
  checksum: 7e8e69b76e892c305071a4736131fe18
  content_type: application/pdf
  creator: cchlebak
  date_created: 2022-01-19T09:41:14Z
  date_updated: 2022-01-19T09:41:14Z
  file_id: '10647'
  file_name: 2022_LettersMathPhys_Henheik.pdf
  file_size: 357547
  relation: main_file
  success: 1
file_date_updated: 2022-01-19T09:41:14Z
fulldoi: https://doi.org/10.1007/s11005-021-01494-y
has_accepted_license: '1'
intvolume: '       112'
isi: 1
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '19540'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Local stability of ground states in locally gapped and weakly interacting quantum
  spin systems
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 112
year: '2022'
...