---
_id: '15002'
abstract:
- lang: eng
  text: "The lattice Schwinger model, the discrete version of QED in \r\n1\r\n+\r\n1\r\n
    dimensions, is a well-studied test bench for lattice gauge theories. Here, we
    study the fractal properties of this model. We reveal the self-similarity of the
    ground state, which allows us to develop a recurrent procedure for finding the
    ground-state wave functions and predicting ground-state energies. We present the
    results of recurrently calculating ground-state wave functions using the fractal
    Ansatz and automized software package for fractal image processing. In certain
    parameter regimes, just a few terms are enough for our recurrent procedure to
    predict ground-state energies close to the exact ones for several hundreds of
    sites. Our findings pave the way to understanding the complexity of calculating
    many-body wave functions in terms of their fractal properties as well as finding
    new links between condensed matter and high-energy lattice models."
acknowledgement: "We thank A. Bargov, I. Khaymovich, and V. Tiunova for fruitful discussions
  and for useful comments. M. C. B. thanks S. Kühn for discussions about the phase
  structure of the model. A. K. F. thanks V. Gritsev and A. Garkun for insightful
  comments. E. V. P., E. S. T., and A. K. F. are\r\nsupported by the RSF Grant No.
  20-42-05002 (studying the fractal Ansatz) and the Roadmap on Quantum Computing (Contract
  No. 868-1.3-15/15-2021, October 5, 2021; calculating on GS energies). A. K. F. thanks
  the Priority 2030 program at the NIST “MISIS” under the project No. K1-2022-027.
  M. C. B. was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
  Foundation) under Germany’s Excellence Strategy—EXC-2111–390814868."
article_number: '050401'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elena
  full_name: Petrova, Elena
  id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
  last_name: Petrova
- first_name: Egor S.
  full_name: Tiunov, Egor S.
  last_name: Tiunov
- first_name: Mari Carmen
  full_name: Bañuls, Mari Carmen
  last_name: Bañuls
- first_name: Aleksey K.
  full_name: Fedorov, Aleksey K.
  last_name: Fedorov
citation:
  ama: Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. Fractal states of the Schwinger
    model. <i>Physical Review Letters</i>. 2024;132(5). doi:<a href="https://doi.org/10.1103/PhysRevLett.132.050401">10.1103/PhysRevLett.132.050401</a>
  apa: Petrova, E., Tiunov, E. S., Bañuls, M. C., &#38; Fedorov, A. K. (2024). Fractal
    states of the Schwinger model. <i>Physical Review Letters</i>. American Physical
    Society. <a href="https://doi.org/10.1103/PhysRevLett.132.050401">https://doi.org/10.1103/PhysRevLett.132.050401</a>
  chicago: Petrova, Elena, Egor S. Tiunov, Mari Carmen Bañuls, and Aleksey K. Fedorov.
    “Fractal States of the Schwinger Model.” <i>Physical Review Letters</i>. American
    Physical Society, 2024. <a href="https://doi.org/10.1103/PhysRevLett.132.050401">https://doi.org/10.1103/PhysRevLett.132.050401</a>.
  ieee: E. Petrova, E. S. Tiunov, M. C. Bañuls, and A. K. Fedorov, “Fractal states
    of the Schwinger model,” <i>Physical Review Letters</i>, vol. 132, no. 5. American
    Physical Society, 2024.
  ista: Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. 2024. Fractal states of the Schwinger
    model. Physical Review Letters. 132(5), 050401.
  mla: Petrova, Elena, et al. “Fractal States of the Schwinger Model.” <i>Physical
    Review Letters</i>, vol. 132, no. 5, 050401, American Physical Society, 2024,
    doi:<a href="https://doi.org/10.1103/PhysRevLett.132.050401">10.1103/PhysRevLett.132.050401</a>.
  short: E. Petrova, E.S. Tiunov, M.C. Bañuls, A.K. Fedorov, Physical Review Letters
    132 (2024).
date_created: 2024-02-18T23:01:00Z
date_published: 2024-01-30T00:00:00Z
date_updated: 2024-02-26T08:03:31Z
day: '30'
department:
- _id: MaSe
doi: 10.1103/PhysRevLett.132.050401
external_id:
  arxiv:
  - '2201.10220'
intvolume: '       132'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2201.10220
month: '01'
oa: 1
oa_version: Preprint
publication: Physical Review Letters
publication_identifier:
  eissn:
  - 1079-7114
  issn:
  - 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fractal states of the Schwinger model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 132
year: '2024'
...
---
_id: '13138'
abstract:
- lang: eng
  text: "We consider the spin-\r\n1\r\n2\r\n Heisenberg chain (XXX model) weakly perturbed
    away from integrability by an isotropic next-to-nearest neighbor exchange interaction.
    Recently, it was conjectured that this model possesses an infinite tower of quasiconserved
    integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)].
    In this work we first test this conjecture by investigating how the norm of the
    adiabatic gauge potential (AGP) scales with the system size, which is known to
    be a remarkably accurate measure of chaos. We find that for the perturbed XXX
    chain the behavior of the AGP norm corresponds to neither an integrable nor a
    chaotic regime, which supports the conjectured quasi-integrability of the model.
    We then prove the conjecture and explicitly construct the infinite set of quasiconserved
    charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest
    exchange interaction can be viewed as a truncation of an integrable long-range
    deformation of the Heisenberg spin chain."
acknowledgement: "The numerical computations in this work were performed using QuSpin
  [83, 84]. We acknowledge useful discussions with Igor Aleiner, Boris Altshuler,
  Jacopo de Nardis, Anatoli Polkovnikov, and Gora Shlyapnikov. We thank Piotr Sierant
  and Dario Rosa for drawing our attention to Refs. [31, 42, 46] and Ref. [47], respectively.
  We are grateful to an anonymous referee for very useful comments and for drawing
  our attention to Refs. [80, 81]. The work of VG is part of the DeltaITP consortium,
  a program of the Netherlands Organization for Scientific\r\nResearch (NWO) funded
  by the Dutch Ministry of Education, Culture and Science (OCW). VG is also partially
  supported by RSF 19-71-10092. The work of AT was supported by the ERC Starting Grant
  101042293 (HEPIQ). RS acknowledges support from Slovenian Research Agency (ARRS)
  - research programme P1-0402. "
article_number: '184312'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pavel
  full_name: Orlov, Pavel
  last_name: Orlov
- first_name: Anastasiia
  full_name: Tiutiakina, Anastasiia
  last_name: Tiutiakina
- first_name: Rustem
  full_name: Sharipov, Rustem
  last_name: Sharipov
- first_name: Elena
  full_name: Petrova, Elena
  id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
  last_name: Petrova
- first_name: Vladimir
  full_name: Gritsev, Vladimir
  last_name: Gritsev
- first_name: Denis V.
  full_name: Kurlov, Denis V.
  last_name: Kurlov
citation:
  ama: Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. Adiabatic
    eigenstate deformations and weak integrability breaking of Heisenberg chain. <i>Physical
    Review B</i>. 2023;107(18). doi:<a href="https://doi.org/10.1103/PhysRevB.107.184312">10.1103/PhysRevB.107.184312</a>
  apa: Orlov, P., Tiutiakina, A., Sharipov, R., Petrova, E., Gritsev, V., &#38; Kurlov,
    D. V. (2023). Adiabatic eigenstate deformations and weak integrability breaking
    of Heisenberg chain. <i>Physical Review B</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevB.107.184312">https://doi.org/10.1103/PhysRevB.107.184312</a>
  chicago: Orlov, Pavel, Anastasiia Tiutiakina, Rustem Sharipov, Elena Petrova, Vladimir
    Gritsev, and Denis V. Kurlov. “Adiabatic Eigenstate Deformations and Weak Integrability
    Breaking of Heisenberg Chain.” <i>Physical Review B</i>. American Physical Society,
    2023. <a href="https://doi.org/10.1103/PhysRevB.107.184312">https://doi.org/10.1103/PhysRevB.107.184312</a>.
  ieee: P. Orlov, A. Tiutiakina, R. Sharipov, E. Petrova, V. Gritsev, and D. V. Kurlov,
    “Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg
    chain,” <i>Physical Review B</i>, vol. 107, no. 18. American Physical Society,
    2023.
  ista: Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. 2023.
    Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg
    chain. Physical Review B. 107(18), 184312.
  mla: Orlov, Pavel, et al. “Adiabatic Eigenstate Deformations and Weak Integrability
    Breaking of Heisenberg Chain.” <i>Physical Review B</i>, vol. 107, no. 18, 184312,
    American Physical Society, 2023, doi:<a href="https://doi.org/10.1103/PhysRevB.107.184312">10.1103/PhysRevB.107.184312</a>.
  short: P. Orlov, A. Tiutiakina, R. Sharipov, E. Petrova, V. Gritsev, D.V. Kurlov,
    Physical Review B 107 (2023).
date_created: 2023-06-18T22:00:46Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-08-02T06:16:02Z
day: '01'
department:
- _id: GradSch
doi: 10.1103/PhysRevB.107.184312
external_id:
  arxiv:
  - '2303.00729'
  isi:
  - '001003686900004'
intvolume: '       107'
isi: 1
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2303.00729
month: '05'
oa: 1
oa_version: Preprint
publication: Physical Review B
publication_identifier:
  eissn:
  - 2469-9969
  issn:
  - 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg
  chain
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 107
year: '2023'
...