---
_id: '13317'
abstract:
- lang: eng
  text: We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables
    in a typical translation invariant system of quantum spins with L-body interactions,
    where L is the number of spins. This mathematically verifies the observation first
    made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130)
    that the ETH may hold for systems with additional translational symmetries for
    a naturally restricted class of observables. We also present numerical support
    for the same phenomenon for Hamiltonians with local interaction.
acknowledgement: "LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond”
  No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan
  Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics
  Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study
  (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The
  University of Tokyo."
article_number: '128'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Shoki
  full_name: Sugimoto, Shoki
  last_name: Sugimoto
- 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: Volodymyr
  full_name: Riabov, Volodymyr
  id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
  last_name: Riabov
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis
    for translation invariant spin systems. <i>Journal of Statistical Physics</i>.
    2023;190(7). doi:<a href="https://doi.org/10.1007/s10955-023-03132-4">10.1007/s10955-023-03132-4</a>
  apa: Sugimoto, S., Henheik, S. J., Riabov, V., &#38; Erdös, L. (2023). Eigenstate
    thermalisation hypothesis for translation invariant spin systems. <i>Journal of
    Statistical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s10955-023-03132-4">https://doi.org/10.1007/s10955-023-03132-4</a>
  chicago: Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös.
    “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.”
    <i>Journal of Statistical Physics</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s10955-023-03132-4">https://doi.org/10.1007/s10955-023-03132-4</a>.
  ieee: S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation
    hypothesis for translation invariant spin systems,” <i>Journal of Statistical
    Physics</i>, vol. 190, no. 7. Springer Nature, 2023.
  ista: Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation
    hypothesis for translation invariant spin systems. Journal of Statistical Physics.
    190(7), 128.
  mla: Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation
    Invariant Spin Systems.” <i>Journal of Statistical Physics</i>, vol. 190, no.
    7, 128, Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s10955-023-03132-4">10.1007/s10955-023-03132-4</a>.
  short: S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics
    190 (2023).
date_created: 2023-07-30T22:01:02Z
date_published: 2023-07-21T00:00:00Z
date_updated: 2023-12-13T11:38:44Z
day: '21'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1007/s10955-023-03132-4
ec_funded: 1
external_id:
  arxiv:
  - '2304.04213'
  isi:
  - '001035677200002'
file:
- access_level: open_access
  checksum: c2ef6b2aecfee1ad6d03fab620507c2c
  content_type: application/pdf
  creator: dernst
  date_created: 2023-07-31T07:49:31Z
  date_updated: 2023-07-31T07:49:31Z
  file_id: '13325'
  file_name: 2023_JourStatPhysics_Sugimoto.pdf
  file_size: 612755
  relation: main_file
  success: 1
file_date_updated: 2023-07-31T07:49:31Z
has_accepted_license: '1'
intvolume: '       190'
isi: 1
issue: '7'
language:
- iso: eng
month: '07'
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: Journal of Statistical Physics
publication_identifier:
  eissn:
  - 1572-9613
  issn:
  - 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Eigenstate thermalisation hypothesis for translation invariant 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: 190
year: '2023'
...