---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '21501'
abstract:
- lang: eng
  text: "Kinetically constrained models were originally introduced to capture slow
    relaxation in glassy systems, where dynamics are hindered by local constraints
    instead of energy barriers. Their quantum counterparts have recently drawn attention
    for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming
    from chiral symmetry. Yet, the structure and implications of these zero modes
    remain poorly understood. In this work, we focus on the properties of the zero
    mode subspace in quantum kinetically constrained models with a U(1) particle-conservation
    symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric
    U(1) East-West models to illustrate our two main results. First, we observe that
    the simultaneous presence of constraints and chiral symmetry generally leads to
    a parametric increase in the number of zero modes due to the fragmentation of
    the many-body\r\nHilbert space into disconnected sectors. Second, we generalize
    the concept of compact localized states from single-particle physics and introduce
    the notion of collective bound states, a special kind of nonergodic eigenstates
    that are robust to enlarging the system size. We formulate sufficient criteria
    for their existence, arguing that the degenerate zero mode subspace plays a central
    role, and demonstrate bound states in both example models and in a two-dimensional
    model, the U(1) North-East, and in the pairflip model, a system without particle
    conservation. Our results motivate a systematic study of bound states and their
    relation to ergodicity breaking, transport, and other properties of quantum kinetically
    constrained\r\nmodels. "
acknowledgement: The authors acknowledge useful discussions with Berislav Buca. This
  work was supported by the European Research Council (ERC) under the European Union’s
  Horizon 2020 research and innovation program (Grant Agreement No. 850899). M.L.
  acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research
  Foundation) under Germany’s Excellence Strategy—EXC-2111—390814868. This research
  was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical
  Physics (KITP).
article_number: '010352'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Eulalia
  full_name: Nicolau Jimenez, Eulalia
  id: 04b4791c-8fd7-11ee-a7df-be2fdc569c48
  last_name: Nicolau Jimenez
- first_name: Marko
  full_name: Ljubotina, Marko
  id: F75EE9BE-5C90-11EA-905D-16643DDC885E
  last_name: Ljubotina
  orcid: 0000-0003-0038-7068
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
citation:
  ama: Nicolau Jimenez E, Ljubotina M, Serbyn M. Fragmentation, zero modes, and collective
    bound states in constrained models. <i>PRX Quantum</i>. 2026;7. doi:<a href="https://doi.org/10.1103/sl79-1xgb">10.1103/sl79-1xgb</a>
  apa: Nicolau Jimenez, E., Ljubotina, M., &#38; Serbyn, M. (2026). Fragmentation,
    zero modes, and collective bound states in constrained models. <i>PRX Quantum</i>.
    American Physical Society. <a href="https://doi.org/10.1103/sl79-1xgb">https://doi.org/10.1103/sl79-1xgb</a>
  chicago: Nicolau Jimenez, Eulalia, Marko Ljubotina, and Maksym Serbyn. “Fragmentation,
    Zero Modes, and Collective Bound States in Constrained Models.” <i>PRX Quantum</i>.
    American Physical Society, 2026. <a href="https://doi.org/10.1103/sl79-1xgb">https://doi.org/10.1103/sl79-1xgb</a>.
  ieee: E. Nicolau Jimenez, M. Ljubotina, and M. Serbyn, “Fragmentation, zero modes,
    and collective bound states in constrained models,” <i>PRX Quantum</i>, vol. 7.
    American Physical Society, 2026.
  ista: Nicolau Jimenez E, Ljubotina M, Serbyn M. 2026. Fragmentation, zero modes,
    and collective bound states in constrained models. PRX Quantum. 7, 010352.
  mla: Nicolau Jimenez, Eulalia, et al. “Fragmentation, Zero Modes, and Collective
    Bound States in Constrained Models.” <i>PRX Quantum</i>, vol. 7, 010352, American
    Physical Society, 2026, doi:<a href="https://doi.org/10.1103/sl79-1xgb">10.1103/sl79-1xgb</a>.
  short: E. Nicolau Jimenez, M. Ljubotina, M. Serbyn, PRX Quantum 7 (2026).
corr_author: '1'
date_created: 2026-03-28T14:57:56Z
date_published: 2026-03-13T00:00:00Z
date_updated: 2026-03-30T06:09:28Z
day: '13'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1103/sl79-1xgb
ec_funded: 1
external_id:
  arxiv:
  - '2504.17627'
file:
- access_level: open_access
  checksum: d155ffa9e1a8275702149165f4bf963c
  content_type: application/pdf
  creator: dernst
  date_created: 2026-03-30T06:08:07Z
  date_updated: 2026-03-30T06:08:07Z
  file_id: '21505'
  file_name: 2026_PRXQuantum_Nicolau.pdf
  file_size: 1848724
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  success: 1
file_date_updated: 2026-03-30T06:08:07Z
has_accepted_license: '1'
intvolume: '         7'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
  call_identifier: H2020
  grant_number: '850899'
  name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: PRX Quantum
publication_identifier:
  eissn:
  - 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fragmentation, zero modes, and collective bound states in constrained models
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: 7
year: '2026'
...