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Cited by 195Quantum many-body systemsBlack Holes and Theoretical PhysicsQuantum chaos and dynamical systems

Power-law out of time order correlation functions in the SYK model

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Bagrets, Dmitry, Altland, Alexander, Kamenev, Alex·2017·Nuclear Physics B
DOI 10.1016/j.nuclphysb.2017.06.012
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Abstract

We evaluate the finite temperature partition sum and correlation functions of the Sachdev–Ye–Kitaev (SYK) model. Starting from a recently proposed mapping of the SYK model onto Liouville quantum mechanics, we obtain our results by exact integration over conformal Goldstone modes reparameterizing physical time. Perhaps, the least expected result of our analysis is that at time scales proportional to the number of particles the out of time order correlation function crosses over from a regime of exponential decay to a universal t − 6 power-law behavior.

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  • At very late times when quantum effects are important, the four-point function decays as a power law when , similarly to the two-point function.

    “Finally, at very late times when quantum effects are important, the four-point function decays as when , similarly to the two-point function. Again this late-time power law was derived before knowing the complete answer by Bagrets et al. (2017).”

    From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Bagrets et al. (2017)

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Research works printed but not linked: 21

  1. [5][5] Vladimir Polchinski, Josephand Rosenhaus. The spectrum in the Sachdev-Ye-Kitaev model. Journal of High Energy Physics , 2016(4):1, 2016. -
  2. [6][6] Juan Maldacena, Douglas Stanford, and Zhenbin Yang. Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space. Progress of Theoretical and Experimental Physics , 2016(12):12C104, 2016. -
  3. [8][8] Micha Berkooz, Prithvi Narayan, Moshe Rozali, and Joan Sim´ on. Higher dimensional generalizations of the SYK model. Journal of High Energy Physics , 2017(1):138, 2017. -
  4. [10][10] J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka. Black Holes and Random Matrices. ArXiv e-prints , 1611.04650, nov 2016. - · arXiv
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  6. [13][13] A. M. Garc´ ıa-Garc´ ıa and J. J. M. Verbaarschot. Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N. ArXiv e-prints , 1701.06593, jan 2017. - · arXiv
  7. [14][14] Julius Engels¨ oy, Thomas G. Mertens, and Herman Verlinde. An investigation of AdS2 backreaction and holography. Journal of High Energy Physics , 2016(7):139, 2016. -
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  9. [18][18] G. Turiaci and H. Verlinde. Towards a 2d QFT Analog of the SYK Model. ArXiv e-prints , 1701.00528, jan 2017. - · arXiv
  10. [19][19] E. Witten. An SYK-Like Model Without Disorder. ArXiv e-prints , 1610.09758, oct 2016. - · arXiv
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  14. [25][25] Y. Liu, M. A. Nowak, and I. Zahed. Disorder in the Sachdev-Ye-Kitaev Model. ArXiv e-prints , 1612.05233, dec 2016. - · arXiv
  15. [28][28] Richard J. Szabo. Equivariant Cohomology and Localization of Path Integrals . Springer, Berlin-Heidelberg, 2000. -
  16. [29][29] I. L. Aleiner, L. Faoro, and L. B. Io e. Microscopic model of quantum butterfly e ect: Out-of-time-order correlators and traveling combustion waves. Annals of Physics , 375:378-406, dec 2016. -
  17. [30][30] Pasquale Calabrese and John Cardy. Quantum quenches in 1 + 1 dimensional conformal field theories. Journal of Statistical Mechanics: Theory and Experiment , 2016(6):064003, 2016. -
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  20. [33][33] J. J. Duistermaat and G. J. Heckman. On the variation in the cohomology of the symplectic form of the reduced phase space. Inventiones mathematicae , 69(2):259-268, 1982. -
  21. [34][34] Hagen Kleinert. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets . World Scientific, Singapore, 2009.

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Authors
Bagrets, D., Altland, A., & Kamenev, A.
Affiliations
  • University of Cologne (DE)
  • University of Minnesota (US)
Corresponding author
Bagrets, Dmitry
ORCID
Venue
Nuclear Physics B
Publisher
Elsevier BV
Published
2017-08
Volume
921
Pages
727-752
ISSN
0550-3213 (ISSN-L)
DOI
10.1016/j.nuclphysb.2017.06.012
OpenAlex
W2591965455
Cited by
195
References
4
Citations by year
2026: 5 · 2025: 9 · 2024: 9 · 2023: 24 · 2022: 30 · 2021: 22 · 2020: 17 · 2019: 34 · 2018: 33 · 2017: 12
FWCI
12.88
Type
journal article
Language
en
Open access
Licence
Locations
  • Nuclear Physics B (publishedVersion, cc-by)
  • Kölner Universitäts PublikationsServer (Universität zu Köln) (publishedVersion)
  • arXiv (Cornell University) (acceptedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • DOE (DEFG02-08ER46482)
  • Cologne University (QM2)
  • Deutsche Forschungsgemeinschaft (CRC 183)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
Keywords
Sachdev-Ye-Kitaev model, power-law decay, quantum chaos

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