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Many-body quantum chaos and space-time translational invariance

Author

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  • 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
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    References listed on IDEAS

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    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.
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