- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Hilbert space fragmentation in a driven-dephasing Rydberg atom array

Tianyi Yan*, Chun Hei Leung, and Weibin Li

  • School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Nonequilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom

  • *Contact author: tianyi.yan@nottingham.ac.uk
PDF

Phys. Rev. Research 8, L032015 – Published 28 July, 2026

DOI: https://doi.org/10.1103/691w-6cx8

Abstract

We investigate the onset and mechanism of Hilbert space fragmentation (HSF) in a chain of strongly interacting Rydberg atoms subjected to local dephasing. It is found that the emergence of multiple long-lived metastable states is fundamentally tied to the HSF of the driven-dephasing Rydberg atom system. We demonstrate that the dephasing PXP model, the effective constrained model for strongly blockaded Rydberg atoms, captures the manifesting HSF and supports multiple degenerate zero modes. These modes form disconnected block-diagonal subspaces of maximally mixed states, which consist of many-body spin states sharing the same symmetry. A key result is the identification of the underlying symmetry in the HSF, where the conserved quantities in each subspace are defined by the consecutive double excitation addressing operator. Moreover, we show explicitly that the number of fragmented Hilbert spaces grows exponentially with the chain length, following a modified Fibonacci sequence. Our work provides insights into many-body dynamics under dynamical constraints and opens avenues for controlling and manipulating HSF in Rydberg atom systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (81)

  1. P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Pollmann, Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians, Phys. Rev. X 10, 011047 (2020).
  2. V. Khemani, M. Hermele, and R. Nandkishore, Localization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020).
  3. S. Roy and A. Lazarides, Strong ergodicity breaking due to local constraints in a quantum system, Phys. Rev. Res. 2, 023159 (2020).
  4. Z.-C. Yang, F. Liu, A. V. Gorshkov, and T. Iadecola, Hilbert-space fragmentation from strict confinement, Phys. Rev. Lett. 124, 207602 (2020).
  5. D. Hahn, P. A. McClarty, and D. J. Luitz, Information dynamics in a model with Hilbert space fragmentation, SciPost Phys. 11, 074 (2021).
  6. S. Moudgalya and O. I. Motrunich, Hilbert space fragmentation and commutant algebras, Phys. Rev. X 12, 011050 (2022).
  7. S. Moudgalya, B. A. Bernevig, and N. Regnault, Quantum many-body scars and Hilbert space fragmentation: A review of exact results, Rep. Prog. Phys. 85, 086501 (2022).
  8. R. Moessner and S. L. Sondhi, Ising models of quantum frustration, Phys. Rev. B 63, 224401 (2001).
  9. P. Fendley, K. Sengupta, and S. Sachdev, Competing density-wave orders in a one-dimensional hard-boson model, Phys. Rev. B 69, 075106 (2004).
  10. I. Lesanovsky, Many-body spin interactions and the ground state of a dense Rydberg lattice gas, Phys. Rev. Lett. 106, 025301 (2011).
  11. V. Khemani, C. R. Laumann, and A. Chandran, Signatures of integrability in the dynamics of Rydberg-blockaded chains, Phys. Rev. B 99, 161101(R) (2019).
  12. S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papić, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent SU(2) dynamics and perfect quantum many-body scars, Phys. Rev. Lett. 122, 220603 (2019).
  13. C.-J. Lin, A. Chandran, and O. I. Motrunich, Slow thermalization of exact quantum many-body scar states under perturbations, Phys. Rev. Res. 2, 033044 (2020).
  14. R. Verresen, M. D. Lukin, and A. Vishwanath, Prediction of toric code topological order from Rydberg blockade, Phys. Rev. X 11, 031005 (2021).
  15. V. Karle, M. Serbyn, and A. A. Michailidis, Area-law entangled eigenstates from nullspaces of local Hamiltonians, Phys. Rev. Lett. 127, 060602 (2021).
  16. F. M. Surace, M. Votto, E. G. Lazo, A. Silva, M. Dalmonte, and G. Giudici, Exact many-body scars and their stability in constrained quantum chains, Phys. Rev. B 103, 104302 (2021).
  17. G.-X. Su, H. Sun, A. Hudomal, J.-Y. Desaules, Z.-Y. Zhou, B. Yang, J. C. Halimeh, Z.-S. Yuan, Z. Papić, and J.-W. Pan, Observation of many-body scarring in a Bose-Hubbard quantum simulator, Phys. Rev. Res. 5, 023010 (2023).
  18. A. N. Ivanov and O. I. Motrunich, Volume-entangled exact scar states in the PXP and related models in any dimension, Phys. Rev. Lett. 134, 050403 (2025).
  19. A. Kerschbaumer, M. Ljubotina, M. Serbyn, and J.-Y. Desaules, Quantum many-body scars beyond the PXP model in Rydberg simulators, Phys. Rev. Lett. 134, 160401 (2025).
  20. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  21. D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuletić, and M. D. Lukin, Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021).
  22. M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010).
  23. X.-Q. Shao, S.-L. Su, L. Li, R. Nath, J.-H. Wu, and W. Li, Rydberg superatoms: An artificial quantum system for quantum information processing and quantum optics, Appl. Phys. Rev. 11, 031320 (2024).
  24. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  25. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  26. M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature (London) 452, 854 (2008).
  27. A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
  28. L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016).
  29. R. G. Palmer, D. L. Stein, E. Abrahams, and P. W. Anderson, Models of hierarchically constrained dynamics for glassy relaxation, Phys. Rev. Lett. 53, 958 (1984).
  30. G. H. Fredrickson and H. C. Andersen, Kinetic Ising model of the glass transition, Phys. Rev. Lett. 53, 1244 (1984).
  31. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  32. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018).
  33. C.-J. Lin and O. I. Motrunich, Exact quantum many-body scar states in the Rydberg-blockaded atom chain, Phys. Rev. Lett. 122, 173401 (2019).
  34. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  35. Z. Yao, L. Pan, S. Liu, and H. Zhai, Quantum many-body scars and quantum criticality, Phys. Rev. B 105, 125123 (2022).
  36. A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Quantum many-body scars: A quasiparticle perspective, Annu. Rev. Condens. Matter Phys. 14, 443 (2023).
  37. G. De Tomasi, D. Hetterich, P. Sala, and F. Pollmann, Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization, Phys. Rev. B 100, 214313 (2019).
  38. S. Moudgalya, A. Prem, R. Nandkishore, N. Regnault, and B. A. Bernevig, Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian, in Memorial Volume for Shoucheng Zhang, edited by B. Lian, C. X. Liu, E. Demler, S. Kivelson, and X. Qi (World Scientific, Singapore, 2021), p. 147.
  39. C. M. Langlett and S. Xu, Hilbert space fragmentation and exact scars of generalized Fredkin spin chains, Phys. Rev. B 103, L220304 (2021).
  40. B. Pozsgay, T. Gombor, A. Hutsalyuk, Y. Jiang, L. Pristyák, and E. Vernier, Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics, Phys. Rev. E 104, 044106 (2021).
  41. E. V. H. Doggen, I. V. Gornyi, and D. G. Polyakov, Stark many-body localization: Evidence for Hilbert-space shattering, Phys. Rev. B 103, L100202 (2021).
  42. T. Rakovszky, P. Sala, R. Verresen, M. Knap, and F. Pollmann, Statistical localization: From strong fragmentation to strong edge modes, Phys. Rev. B 101, 125126 (2020).
  43. B. Mukherjee, D. Banerjee, K. Sengupta, and A. Sen, Minimal model for Hilbert space fragmentation with local constraints, Phys. Rev. B 104, 155117 (2021).
  44. T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Exploring the regime of fragmentation in strongly tilted Fermi-Hubbard chains, Phys. Rev. Lett. 130, 010201 (2023).
  45. E. Nicolau, A. M. Marques, J. Mompart, V. Ahufinger, and R. G. Dias, Local Hilbert space fragmentation and weak thermalization in Bose-Hubbard diamond necklaces, Phys. Rev. B 107, 094312 (2023).
  46. G. Francica and L. Dell’Anna, Hilbert space fragmentation in a long-range system, Phys. Rev. B 108, 045127 (2023).
  47. P. Brighi, M. Ljubotina, and M. Serbyn, Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models, SciPost Phys. 15, 093 (2023).
  48. R. J. Valencia-Tortora, N. Pancotti, M. Fleischhauer, H. Bernien, and J. Marino, Rydberg platform for nonergodic chiral quantum dynamics, Phys. Rev. Lett. 132, 223201 (2024).
  49. S. Aditya, D. Dhar, and D. Sen, Subspace-restricted thermalization in a correlated-hopping model with strong Hilbert space fragmentation characterized by irreducible strings, Phys. Rev. B 110, 045418 (2024).
  50. M. Ganguli, S. Aditya, and D. Sen, Aspects of Hilbert space fragmentation in the quantum East model: Fragmentation, subspace-restricted quantum scars, and effects of density-density interactions, Phys. Rev. B 111, 045411 (2025).
  51. F. Yang, H. Yarloo, H.-C. Zhang, K. Mølmer, and A. E. B. Nielsen, Probing Hilbert space fragmentation with strongly interacting Rydberg atoms, Phys. Rev. B 111, 144313 (2025).
  52. D. Adler, D. Wei, M. Will, K. Srakaew, S. Agrawal, P. Weckesser, R. Moessner, F. Pollmann, I. Bloch, and J. Zeiher, Observation of Hilbert space fragmentation and fractonic excitations in 2D, Nature (London) 636, 80 (2024).
  53. K. Honda, Y. Takasu, S. Goto, H. Kazuta, M. Kunimi, I. Danshita, and Y. Takahashi, Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains, Sci. Adv. 11, eadv3255 (2025).
  54. Y.-Y. Wang et al., Exploring Hilbert-space fragmentation on a superconducting processor, PRX Quantum 6, 010325 (2025).
  55. L. Zhao, P. R. Datla, W. Tian, M. M. Aliyu, and H. Loh, Observation of quantum thermalization restricted to Hilbert space fragments and Z2k scars, Phys. Rev. X 15, 011035 (2025).
  56. Y. Li, P. Sala, and F. Pollmann, Hilbert space fragmentation in open quantum systems, Phys. Rev. Res. 5, 043239 (2023).
  57. A. Marché, G. Morettini, L. Mazza, L. Gotta, and L. Capizzi, Exceptional stationary state in a dephasing many-body open quantum system, Phys. Rev. Lett. 135, 020406 (2025).
  58. H. Li and W. Yi, Symmetry-induced fragmentation and dissipative time crystal, Phys. Rev. B 113, 014316 (2026).
  59. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  60. S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum phases of matter on a 256-atom programmable quantum simulator, Nature (London) 595, 227 (2021).
  61. J. Honer, R. Löw, H. Weimer, T. Pfau, and H. P. Büchler, Artificial atoms can do more than atoms: Deterministic single photon subtraction from arbitrary light fields, Phys. Rev. Lett. 107, 093601 (2011).
  62. S. Helmrich, A. Arias, and S. Whitlock, Uncovering the nonequilibrium phase structure of an open quantum spin system, Phys. Rev. A 98, 022109 (2018).
  63. L. M. Sieberer, M. Buchhold, J. Marino, and S. Diehl, Universality in driven open quantum matter, Rev. Mod. Phys. 97, 025004 (2025).
  64. I. Lesanovsky and J. P. Garrahan, Kinetic constraints, hierarchical relaxation, and onset of glassiness in strongly interacting and dissipative Rydberg gases, Phys. Rev. Lett. 111, 215305 (2013).
  65. M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, Universal nonequilibrium properties of dissipative Rydberg gases, Phys. Rev. Lett. 113, 210401 (2014).
  66. M. Hoening, W. Abdussalam, M. Fleischhauer, and T. Pohl, Antiferromagnetic long-range order in dissipative Rydberg lattices, Phys. Rev. A 90, 021603(R) (2014).
  67. M. Marcuzzi, E. Levi, W. Li, J. P. Garrahan, B. Olmos, and I. Lesanovsky, Non-equilibrium universality in the dynamics of dissipative cold atomic gases, New J. Phys. 17, 072003 (2015).
  68. S. Helmrich, A. Arias, G. Lochead, T. M. Wintermantel, M. Buchhold, S. Diehl, and S. Whitlock, Signatures of self-organized criticality in an ultracold atomic gas, Nature (London) 577, 481 (2020).
  69. J. Kazemi and H. Weimer, Driven-dissipative Rydberg blockade in optical lattices, Phys. Rev. Lett. 130, 163601 (2023).
  70. K. Macieszczak, M. Guţă, I. Lesanovsky, and J. P. Garrahan, Towards a theory of metastability in open quantum dynamics, Phys. Rev. Lett. 116, 240404 (2016).
  71. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, UK, 2007).
  72. L.-N. Wu and A. Eckardt, Prethermal memory loss in interacting quantum systems coupled to thermal baths, Phys. Rev. B 101, 220302 (2020).
  73. S. Saha and R. Bhattacharyya, Prethermalization in an open quantum system coupled to a spatially correlated bosonic bath, J. Stat. Mech. (2024) 023103.
  74. S. Artini, M. Paternostro, and S. Lorenzo, Coherent heat exchange in a prethermalizing open quantum system, Phys. Rev. A 113, 052203 (2026).
  75. See Supplemental Material at http://link.aps.org/supplemental/10.1103/691w-6cx8 for details on the derivation of the dPXP model, mean field results, recursive relation and scaling of f(L), and dynamics of different chain lengths, which includes Refs. [6, 10, 57, 76].
  76. I. Lesanovsky and H. Katsura, Interacting Fibonacci anyons in a Rydberg gas, Phys. Rev. A 86, 041601(R) (2012).
  77. T. Chen, C. Huang, J. P. Covey, and B. Gadway, Collective dissipation engineering of interacting Rydberg atoms, arXiv:2509.06373.
  78. Y.-W. Zhang, B. Xu, Y. Zhou, D.-S. Xiang, H.-X. Liu, P. Zhou, K. Zhang, R. Liao, T. Pohl, W. Li, and L. Li, Observation of non-Hermitian many-body phase transition in a Rydberg-atom array, arXiv:2512.02753.
  79. A. Moharramipour, L. A. Lessa, C. Wang, T. H. Hsieh, and S. Sahu, Symmetry-enforced entanglement in maximally mixed states, PRX Quantum 5, 040336 (2024).
  80. L. Herviou, J. H. Bardarson, and N. Regnault, Many-body localization in a fragmented Hilbert space, Phys. Rev. B 103, 134207 (2021).
  81. T. Yan, C. Leung, and W. Li, Hilbert space fragmentation in driven-dephasing Rydberg atom array, Zenodo, 2025, https://doi.org/10.5281/zenodo.17769423.

Outline

Information

Phys. Rev. Research 8, L032015– Published 28 July, 2026
  • Received 19 December 2025
  • Accepted 25 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation