IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v13y2022i1d10.1038_s41467-022-34318-1.html
   My bibliography  Save this article

Many-body quantum chaos and space-time translational invariance

Author

Listed:
  • Amos Chan

    (Princeton Center for Theoretical Science, Princeton University
    Lancaster University)

  • Saumya Shivam

    (Princeton University)

  • David A. Huse

    (Princeton University)

  • Andrea De Luca

    (Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS)

Abstract

We study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q. At sufficiently large t, diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) behaviour. At finite t, we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both t and L are large while the ratio between L and LTh(t), the many-body Thouless length, is fixed. We numerically demonstrate, with simulations of two distinct circuit models, that the resulting scaling functions are universal in the scaling limit.

Suggested Citation

  • Amos Chan & Saumya Shivam & David A. Huse & Andrea De Luca, 2022. "Many-body quantum chaos and space-time translational invariance," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-34318-1
    DOI: 10.1038/s41467-022-34318-1
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-022-34318-1
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/s41467-022-34318-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Marcos Rigol & Vanja Dunjko & Maxim Olshanii, 2008. "Thermalization and its mechanism for generic isolated quantum systems," Nature, Nature, vol. 452(7189), pages 854-858, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefan Birnkammer & Alvise Bastianello & Michael Knap, 2022. "Prethermalization in one-dimensional quantum many-body systems with confinement," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    2. Durga Bhaktavatsala Rao Dasari & Sen Yang & Arnab Chakrabarti & Amit Finkler & Gershon Kurizki & Jörg Wrachtrup, 2022. "Anti-Zeno purification of spin baths by quantum probe measurements," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    3. Takato Yoshimura & Lucas Sá, 2024. "Robustness of quantum chaos and anomalous relaxation in open quantum circuits," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    4. Shayan Majidy, 2024. "Noncommuting charges can remove non-stationary quantum many-body dynamics," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    5. Lennart Dabelow & Peter Reimann, 2024. "Stalled response near thermal equilibrium in periodically driven systems," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    6. Filiberto Ares & Sara Murciano & Pasquale Calabrese, 2023. "Entanglement asymmetry as a probe of symmetry breaking," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    7. F. H. B. Somhorst & R. Meer & M. Correa Anguita & R. Schadow & H. J. Snijders & M. Goede & B. Kassenberg & P. Venderbosch & C. Taballione & J. P. Epping & H. H. Vlekkert & J. Timmerhuis & J. F. F. Bul, 2023. "Quantum simulation of thermodynamics in an integrated quantum photonic processor," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    8. Lozano-Negro, Fabricio S. & Zangara, Pablo R. & Pastawski, Horacio M., 2021. "Ergodicity breaking in an incommensurate system observed by OTOCs and loschmidt echoes: From quantum diffusion to sub-diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Liang Xiang & Jiachen Chen & Zitian Zhu & Zixuan Song & Zehang Bao & Xuhao Zhu & Feitong Jin & Ke Wang & Shibo Xu & Yiren Zou & Hekang Li & Zhen Wang & Chao Song & Alexander Yue & Justine Partridge & , 2024. "Enhanced quantum state transfer by circumventing quantum chaotic behavior," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    10. Garrahan, Juan P., 2018. "Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 130-154.
    11. Shraddha Sharma & Tanay Nag & Atanu Rajak & Souvik Bandyopadhyay & Sourav Bhattacharjee & Somnath Maity & Utso Bhattacharya, 2024. "Unquenched—a memoir on non-equilibrium dynamics of quantum many-body systems: honoring Amit Dutta," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(7), pages 1-16, July.
    12. Sourav Bhattacharjee & Souvik Bandyopadhyay & Anatoli Polkovnikov, 2024. "Sharp detection of the onset of Floquet heating using eigenstate sensitivity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(10), pages 1-15, October.
    13. Matsuyama, Kazue, 2021. "Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    14. Lih-King Lim & Cunzhong Lou & Chushun Tian, 2024. "Mesoscopic fluctuations in entanglement dynamics," Nature Communications, Nature, vol. 15(1), pages 1-8, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-34318-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.