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Correlation functions and chaotic behavior of the SYK chain model in pure states

Seyyed M. H. Halataei

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Phys. Rev. D 112, 026036 – Published 31 July, 2025

DOI: https://doi.org/10.1103/wwfl-tkwm

Abstract

Recent investigations of Rényi entanglement entropy in the Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions have indicated that the model exhibits slow thermalization when initialized in certain states. The extent to which the heavy modes—believed to underlie this behavior—affect other aspects of the model remains an open question. In this work, I study thermalization and scrambling of information in individual energy eigenstates of the SYK chain using exact diagonalization. I show that two-point correlation functions in finite-energy eigenstates closely match their thermal counterparts and that information scrambling occurs efficiently within these pure states. These results suggest that the slow thermalization observed in entanglement dynamics does not extend to all probes of thermalization and scrambling, even in pure states.

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See Also

Eigenstate thermalization in the two-site SYK and SYK chain models

Seyyed M. H. Halataei
Phys. Rev. D 112, 026016 (2025)

Article Text

References (37)

  1. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  2. Mark Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  3. Mark Srednicki, Thermal fluctuations in quantized chaotic systems, J. Phys. A 29, L75 (1996).
  4. Marcos Rigol, Vanja Dunjko, and Maxim Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature (London) 452, 854 (2008).
  5. Luca D’Alessio, Yariv Kafri, Anatoli Polkovnikov, and Marcos Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016).
  6. Yingfei Gu, Andrew Lucas, and Xiao-Liang Qi, Spread of entanglement in a Sachdev-ye-Kitaev chain, J. High Energy Phys. 09 (2017) 120.
  7. Yingfei Gu, Xiao-Liang Qi, and Douglas Stanford, Local criticality, diffusion and chaos in generalized Sachdev-ye-Kitaev models, J. High Energy Phys. 05 (2017) 125.
  8. Seyyed M. H. Halataei, Eigenstate thermalization in the two-site SYK and SYK chain models, Phys. Rev. D 112, 026016 (2025).
  9. A. Kitaev, A simple model of quantum holography, in KITP Strings Seminar and Entanglement (2015).
  10. Juan Maldacena and Douglas Stanford, Remarks on the Sachdev-ye-Kitaev model, Phys. Rev. D 94, 106002 (2016).
  11. Subir Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5, 041025 (2015).
  12. Alexei Kitaev, A simple model of quantum holography (part 2), in Entanglement in Strongly-Correlated Quantum Matter (2015).
  13. Joseph Polchinski and Vladimir Rosenhaus, The spectrum in the Sachdev-ye-Kitaev model, J. High Energy Phys. 04 (2016) 001.
  14. Juan Maldacena, Stephen H Shenker, and Douglas Stanford, A bound on chaos, J. High Energy Phys. 08 (2016) 001.
  15. S. W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460 (1976).
  16. Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully, Black holes: Complementarity or firewalls?, J. High Energy Phys. 02 (2013) 001.
  17. Geoffrey Penington, Entanglement wedge reconstruction and the information paradox, J. High Energy Phys. 09 (2020) 001.
  18. Ahmed Almheiri, Netta Engelhardt, Donald Marolf, and Henry Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, J. High Energy Phys. 12 (2019) 001.
  19. Ahmed Almheiri, Raghu Mahajan, Juan Maldacena, and Ying Zhao, The page curve of Hawking radiation from semiclassical geometry, J. High Energy Phys. 03 (2020) 001.
  20. Ahmed Almheiri, Raghu Mahajan, and Juan Maldacena, Islands outside the horizon, arXiv:1910.11077.
  21. Ahmed Almheiri, Raghu Mahajan, and Jorge Santos, Entanglement islands in higher dimensions, SciPost Phys. 9, 001 (2020).
  22. Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, and Amirhossein Tajdini, Replica wormholes and the entropy of Hawking radiation, J. High Energy Phys. 05 (2020) 001.
  23. Alishahiha Mohsen, Astaneh Amin Faraji, and Naseh Ali, Island in the presence of higher derivative terms, J. High Energy Phys. 02 (2021) 035.
  24. Raphael Bousso and Marija Tomašević, Unitarity from a smooth horizon?, Phys. Rev. D 102, 106019 (2020).
  25. Phil Saad, Stephen H. Shenker, Douglas Stanford, and Shunyu Yao, Wormholes without averaging, J. High Energy Phys. 09 (2024) 133.
  26. Julian Sonner and Manuel Vielma, Eigenstate thermalization in the Sachdev-ye-Kitaev model, J. High Energy Phys. 11 (2017) 149.
  27. Nicholas Hunter-Jones, Junyu Liu, and Yehao Zhou, On thermalization in the SYK and supersymmetric SYK models, J. High Energy Phys. 02 (2018) 142.
  28. Subir Sachdev and Jinwu Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993).
  29. Gabor Sarosi, Ads2 holography and the SYK model, Proc. Sci. Modave2017 (2018) 001.
  30. Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, Joseph Polchinski, Phil Saad, Stephen H. Shenker, Douglas Stanford, Alexandre Streicher, and Masaki Tezuka, Black holes and random matrices, J. High Energy Phys. 05 (2017) 001.
  31. Richard A. Davison, Wenbo Fu, Antoine Georges, Yingfei Gu, Kristan Jensen, and Subir Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-ye-Kitaev models and holography, Phys. Rev. B 95, 155131 (2017).
  32. Antonio M. García-García, Yiyang Jia, and Jacobus J. M. Verbaarschot, Universality and Thouless energy in the supersymmetric Sachdev-ye-Kitaev model, Phys. Rev. D 97, 106003 (2018).
  33. Wenbo Fu and Subir Sachdev, Numerical study of fermion and boson models with infinite-range random interactions, Phys. Rev. B 94, 035135 (2016).
  34. A. Del Campo, J. Molina-Vilaplana, and J. Sonner, Scrambling the spectral form factor: Unitarity constraints and exact results, Phys. Rev. D 95, 126008 (2017).
  35. E. Brézin and S. Hikami, Spectral form factor in a random matrix theory, Phys. Rev. E 55, 4067 (1997).
  36. Ramanjit Sohal, Laimei Nie, Xiao-Qi Sun, and Eduardo Fradkin, Thermalization of randomly coupled SYK models, J. Stat. Mech. (2022) 013103.
  37. Micha Berkooz, Prithvi Narayan, Moshe Rozali, and Joan Simón, Higher dimensional generalizations of the SYK model, J. High Energy Phys. 01 (2017) 001.

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Phys. Rev. D 112, 026036– Published 31 July, 2025
  • Received 20 May 2025
  • Accepted 16 July 2025
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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. Funded by SCOAP3.

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