---
_id: '5794'
abstract:
- lang: eng
  text: We present an approach to interacting quantum many-body systems based on the
    notion of quantum groups, also known as q-deformed Lie algebras. In particular,
    we show that, if the symmetry of a free quantum particle corresponds to a Lie
    group G, in the presence of a many-body environment this particle can be described
    by a deformed group, Gq. Crucially, the single deformation parameter, q, contains
    all the information about the many-particle interactions in the system. We exemplify
    our approach by considering a quantum rotor interacting with a bath of bosons,
    and demonstrate that extracting the value of q from closed-form solutions in the
    perturbative regime allows one to predict the behavior of the system for arbitrary
    values of the impurity-bath coupling strength, in good agreement with nonperturbative
    calculations. Furthermore, the value of the deformation parameter allows one to
    predict at which coupling strengths rotor-bath interactions result in a formation
    of a stable quasiparticle. The approach based on quantum groups does not only
    allow for a drastic simplification of impurity problems, but also provides valuable
    insights into hidden symmetries of interacting many-particle systems.
article_number: '255302'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Enderalp
  full_name: Yakaboylu, Enderalp
  id: 38CB71F6-F248-11E8-B48F-1D18A9856A87
  last_name: Yakaboylu
  orcid: 0000-0001-5973-0874
- first_name: Mikhail
  full_name: Shkolnikov, Mikhail
  id: 35084A62-F248-11E8-B48F-1D18A9856A87
  last_name: Shkolnikov
  orcid: 0000-0002-4310-178X
- first_name: Mikhail
  full_name: Lemeshko, Mikhail
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
citation:
  ama: Yakaboylu E, Shkolnikov M, Lemeshko M. Quantum groups as hidden symmetries
    of quantum impurities. <i>Physical Review Letters</i>. 2018;121(25). doi:<a href="https://doi.org/10.1103/PhysRevLett.121.255302">10.1103/PhysRevLett.121.255302</a>
  apa: Yakaboylu, E., Shkolnikov, M., &#38; Lemeshko, M. (2018). Quantum groups as
    hidden symmetries of quantum impurities. <i>Physical Review Letters</i>. American
    Physical Society. <a href="https://doi.org/10.1103/PhysRevLett.121.255302">https://doi.org/10.1103/PhysRevLett.121.255302</a>
  chicago: Yakaboylu, Enderalp, Mikhail Shkolnikov, and Mikhail Lemeshko. “Quantum
    Groups as Hidden Symmetries of Quantum Impurities.” <i>Physical Review Letters</i>.
    American Physical Society, 2018. <a href="https://doi.org/10.1103/PhysRevLett.121.255302">https://doi.org/10.1103/PhysRevLett.121.255302</a>.
  ieee: E. Yakaboylu, M. Shkolnikov, and M. Lemeshko, “Quantum groups as hidden symmetries
    of quantum impurities,” <i>Physical Review Letters</i>, vol. 121, no. 25. American
    Physical Society, 2018.
  ista: Yakaboylu E, Shkolnikov M, Lemeshko M. 2018. Quantum groups as hidden symmetries
    of quantum impurities. Physical Review Letters. 121(25), 255302.
  mla: Yakaboylu, Enderalp, et al. “Quantum Groups as Hidden Symmetries of Quantum
    Impurities.” <i>Physical Review Letters</i>, vol. 121, no. 25, 255302, American
    Physical Society, 2018, doi:<a href="https://doi.org/10.1103/PhysRevLett.121.255302">10.1103/PhysRevLett.121.255302</a>.
  short: E. Yakaboylu, M. Shkolnikov, M. Lemeshko, Physical Review Letters 121 (2018).
date_created: 2019-01-06T22:59:12Z
date_published: 2018-12-17T00:00:00Z
date_updated: 2025-04-15T06:50:24Z
day: '17'
department:
- _id: MiLe
doi: 10.1103/PhysRevLett.121.255302
ec_funded: 1
external_id:
  arxiv:
  - '1809.00222'
  isi:
  - '000454178600009'
intvolume: '       121'
isi: 1
issue: '25'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1809.00222
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
- _id: 26031614-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P29902
  name: Quantum rotations in the presence of a many-body environment
publication: Physical Review Letters
publication_identifier:
  issn:
  - '00319007'
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum groups as hidden symmetries of quantum impurities
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 121
year: '2018'
...