- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Weak ergodicity breaking transition in a randomly constrained model

Aydin Deger1,2 and Achilleas Lazarides2

  • 1Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
  • 2Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom

PDF

Phys. Rev. B 109, L220301 – Published 11 June, 2024

DOI: https://doi.org/10.1103/PhysRevB.109.L220301

Abstract

Experiments in Rydberg atoms have recently found unusually slow decay from a small number of special initial states. We investigate the robustness of such long-lived states (LLS) by studying an ensemble of locally constrained random systems with tunable range μ. Upon varying μ, we find a transition between thermal and weakly nonergodic (supporting a finite number of LLS) phases. Furthermore, we demonstrate that the LLS observed in the experiments disappear upon the addition of small perturbations so that the transition reported here is distinct from known ones. We then show that the LLS dynamics explores only part of the accessible Hilbert space, thus corresponding to localization in Hilbert space.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (38)

  1. J. von Neumann, Proof of the ergodic theorem and the H-theorem in quantum mechanics, Eur. Phys. J. H 35, 201 (2010).
  2. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  3. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  4. 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 (2015).
  5. A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices, Phys. Rev. E 54, 3221 (1996).
  6. D. Basko, Hopping between localized Floquet states in periodically driven quantum dots, Phys. Rev. Lett. 91, 206801 (2003).
  7. R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
  8. J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Quantum chaos challenges many-body localization, Phys. Rev. E 102, 062144 (2020).
  9. P. Sierant, D. Delande, and J. Zakrzewski, Thouless time analysis of Anderson and many-body localization transitions, Phys. Rev. Lett. 124, 186601 (2020).
  10. D. Sels and A. Polkovnikov, Dynamical obstruction to localization in a disordered spin chain, Phys. Rev. E 104, 054105 (2021).
  11. D. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Distinguishing localization from chaos: Challenges in finite-size systems, Ann. Phys. 427, 168415 (2021).
  12. P. Sierant and J. Zakrzewski, Challenges to observation of many-body localization, Phys. Rev. B 105, 224203 (2022).
  13. M. Schreiber, S. Hodgman, P. Bordia, H. Lüschen, M. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Quantum gases. observation of many-body localization of interacting fermions in a quasirandom optical lattice, Science 349, 842 (2015).
  14. S. Iyer, V. Oganesyan, G. Refael, and D. A. Huse, Many-body localization in a quasiperiodic system, Phys. Rev. B 87, 134202 (2013).
  15. D. A. Huse, R. Nandkishore, and V. Oganesyan, Phenomenology of fully many-body-localized systems, Phys. Rev. B 90, 174202 (2014).
  16. D. J. Luitz, N. Laflorencie, and F. Alet, Many-body localization edge in the random-field Heisenberg chain, Phys. Rev. B 91, 081103(R) (2015).
  17. 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).
  18. I. Lesanovsky, Many-body spin interactions and the ground state of a dense Rydberg lattice gas, Phys. Rev. Lett. 106, 025301 (2011).
  19. C. Turner, A. Michailidis, D. Abanin, M. Serbyn, and Z. Papic, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  20. 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).
  21. K. Bull, J.-Y. Desaules, and Z. Papić, Quantum scars as embeddings of weakly broken lie algebra representations, Phys. Rev. B 101, 165139 (2020).
  22. K. Bull, I. Martin, and Z. Papić, Systematic construction of scarred many-body dynamics in 1D lattice models, Phys. Rev. Lett. 123, 030601 (2019).
  23. B. Jeevanesan, Quantum scar states in coupled random graph models, Phys. Rev. B 108, 075131 (2023).
  24. B. Buča, Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems, Phys. Rev. X 13, 031013 (2023).
  25. E. J. Heller, Bound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits, Phys. Rev. Lett. 53, 1515 (1984).
  26. 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).
  27. 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).
  28. 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).
  29. J.-Y. Desaules, K. Bull, A. Daniel, and Z. Papić, Hypergrid subgraphs and the origin of scarred quantum walks in many-body Hilbert space, Phys. Rev. B 105, 245137 (2022).
  30. F. M. Surace, M. Dalmonte, and A. Silva, Quantum local random networks and the statistical robustness of quantum scars, SciPost Phys. 14, 174 (2023).
  31. S. Roy and A. Lazarides, Strong ergodicity breaking due to local constraints in a quantum system, Phys. Rev. Res. 2, 023159 (2020).
  32. C. Turner, K. Meichanetzidis, Z. Papić, and J. Pachos, Optimal free descriptions of many-body theories, Nat. Commun. 8, 14926 (2017).
  33. 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).
  34. S. Pai, M. Pretko, and R. M. Nandkishore, Localization in fractonic random circuits, Phys. Rev. X 9, 021003 (2019).
  35. V. Khemani, M. Hermele, and R. M. Nandkishore, Localization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020).
  36. Viewing the spin model as a single-particle hopping problem on a graph, the adjacency matrix of which is the Hamiltonian, not all sites are reachable by allowed hops from all others.
  37. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.109.L220301 for where we describe the construction of the largest connected cluster of the Hamiltonian, display level statistics inside that cluster and show the effect of different LLS thresholds.
  38. Y. A. Alaoui and B. Laburthe-Tolra, A method to discriminate between localized and chaotic quantum systems, arXiv:2307.10706.

Outline

Information

Phys. Rev. B 109, L220301– Published 11 June, 2024
  • Received 18 October 2023
  • Accepted 23 May 2024
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