Skip to main content
SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

On thermalization in the SYK and supersymmetric SYK models

  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 22 February 2018
  • volume 2018, Article number: 142 (2018)
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
On thermalization in the SYK and supersymmetric SYK models
Download PDF
  • Nicholas Hunter-Jones1,
  • Junyu Liu2 &
  • Yehao Zhou3,4 

  • 549 Accesses

  • 25 Citations

  • 2 Altmetric

  • Explore all metrics

  • Cite this article

A preprint version of the article is available at arXiv.

Abstract

The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its \( \mathcal{N} \) = 1 supersymmetric extension and find evidence that these models satisfy ETH. We discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. J.M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991) 2046.

    Article  ADS  MathSciNet  Google Scholar 

  2. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50 (1994) 888.

    ADS  Google Scholar 

  3. M. Rigol, V. Dunjko and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature 452 (2008) 854 [arXiv:0708.1324].

    Article  ADS  Google Scholar 

  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 (2016) 239 [arXiv:1509.06411] [INSPIRE].

    Article  ADS  Google Scholar 

  5. G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  6. M. Srednicki, The approach to thermal equilibrium in quantized chaotic systems, J. Phys. A 32 (1999) 1163 [cond-mat/9809360].

  7. P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  8. Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].

    Article  ADS  Google Scholar 

  9. S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. P. Hosur, X.-L. Qi, D.A. Roberts and B. Yoshida, Chaos in quantum channels, JHEP 02 (2016) 004 [arXiv:1511.04021] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. D.A. Roberts and B. Yoshida, Chaos and complexity by design, JHEP 04 (2017) 121 [arXiv:1610.04903] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. J. Cotler, N. Hunter-Jones, J. Liu and B. Yoshida, Chaos, Complexity and Random Matrices, JHEP 11 (2017) 048 [arXiv:1706.05400] [INSPIRE].

    Article  ADS  Google Scholar 

  13. A. Kitaev, A simple model of quantum holography, talks given at the KITP, 7 Apr. 2015 and 27 May 2015.

  14. S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].

  15. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].

    ADS  Google Scholar 

  16. J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  17. J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  18. S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  19. D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].

    Article  ADS  Google Scholar 

  20. K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].

    Article  ADS  Google Scholar 

  21. J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].

  22. Y.-Z. You, A.W.W. Ludwig and C. Xu, Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States, Phys. Rev. B 95 (2017) 115150 [arXiv:1602.06964] [INSPIRE].

    Article  ADS  Google Scholar 

  23. A.M. García-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].

  24. J.S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S.H. Shenker et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [arXiv:1611.04650] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [Addendum ibid. D 95 (2017) 069904] [arXiv:1610.08917] [INSPIRE].

  26. J.M. Magan, Random free fermions: An analytical example of eigenstate thermalization, Phys. Rev. Lett. 116 (2016) 030401 [arXiv:1508.05339] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  27. A. Eberlein, V. Kasper, S. Sachdev and J. Steinberg, Quantum quench of the Sachdev-Ye-Kitaev Model, Phys. Rev. B 96 (2017) 205123 [arXiv:1706.07803] [INSPIRE].

    Article  Google Scholar 

  28. Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Y. Gu, A. Lucas and X.-L. Qi, Spread of entanglement in a Sachdev-Ye-Kitaev chain, JHEP 09 (2017) 120 [arXiv:1708.00871] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  30. I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS 2 gravity, arXiv:1707.02325 [INSPIRE].

  31. J. Sonner and M. Vielma, Eigenstate thermalization in the Sachdev-Ye-Kitaev model, JHEP 11 (2017) 149 [arXiv:1707.08013] [INSPIRE].

    Article  ADS  Google Scholar 

  32. S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].

    Article  Google Scholar 

  33. W. Fu and S. Sachdev, Numerical study of fermion and boson models with infinite-range random interactions, Phys. Rev. B 94 (2016) 035135 [arXiv:1603.05246] [INSPIRE].

    Article  ADS  Google Scholar 

  34. R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].

    Article  ADS  Google Scholar 

  35. K. Bulycheva, A note on the SYK model with complex fermions, JHEP 12 (2017) 069 [arXiv:1706.07411] [INSPIRE].

    Article  ADS  Google Scholar 

  36. A. Kitaev and J. Suh, Some new results on the Sachdev-Ye-Kitaev model/The bulk dual of the lowest resonance in the Sachdev-Ye-Kitaev model, talks given at Princeton, 21 October 2016, and at the Perimeter Institute, 12 December 2016.

  37. J. Murugan, D. Stanford and E. Witten, More on Supersymmetric and 2d Analogs of the SYK Model, JHEP 08 (2017) 146 [arXiv:1706.05362] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  38. J. Yoon, Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation, JHEP 10 (2017) 172 [arXiv:1706.05914] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  39. C. Peng, M. Spradlin and A. Volovich, Correlators in the \( \mathcal{N} \) = 2 Supersymmetric SYK Model, JHEP 10 (2017) 202 [arXiv:1706.06078] [INSPIRE].

  40. T. Li, J. Liu, Y. Xin and Y. Zhou, Supersymmetric SYK model and random matrix theory, JHEP 06 (2017) 111 [arXiv:1702.01738] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. T. Kanazawa and T. Wettig, Complete random matrix classification of SYK models with \( \mathcal{N} \) = 0, 1 and 2 supersymmetry, JHEP 09 (2017) 050 [arXiv:1706.03044] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  42. C. Peng, M. Spradlin and A. Volovich, A Supersymmetric SYK-like Tensor Model, JHEP 05 (2017) 062 [arXiv:1612.03851] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. M. Srednicki, Thermal fluctuations in quantized chaotic systems, J. Phys. A 29 (1996) L75 [chao-dyn/9511001] [INSPIRE].

  44. J.R. Garrison and T. Grover, Does a single eigenstate encode the full Hamiltonian?, arXiv:1503.00729 [INSPIRE].

  45. L.F. Santos and M. Rigol, Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems, Phys. Rev. E 82 (2010) 031130 [arXiv:1006.0729].

    ADS  MathSciNet  Google Scholar 

  46. M. Rigol and L.F. Santos, Quantum chaos and thermalization in gapped systems, Phys. Rev. A 82 (2010) 011604 [arXiv:1003.1403].

    Article  ADS  Google Scholar 

  47. L.F. Santos and M. Rigol, Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization, Phys. Rev. E 81 (2010) 036206 [arXiv:0910.2985].

    ADS  Google Scholar 

  48. M. Rigol, Quantum quenches and thermalization in one-dimensional fermionic systems, Phys. Rev. A 80 (2009) 053607 [arXiv:0908.3188].

    Article  ADS  Google Scholar 

  49. R. Mondaini, K.R. Fratus, M. Srednicki and M. Rigol, Eigenstate thermalization in the two-dimensional transverse field ising model, Phys. Rev. E 93 (2016) 032104 [arXiv:1512.04947].

    ADS  Google Scholar 

  50. H. Kim, T.N. Ikeda and D.A. Huse, Testing whether all eigenstates obey the eigenstate thermalization hypothesis, Phys. Rev. E 90 (2014) 052105 [arXiv:1408.0535].

    ADS  Google Scholar 

  51. R. Steinigeweg, J. Herbrych, and P. Prelovšek, Eigenstate thermalization within isolated spin-chain systems, Phys. Rev. E 87 (2013) 012118 [arXiv:1208.6143].

    ADS  Google Scholar 

  52. N. Hunter-Jones and J. Liu, Chaos and random matrices in supersymmetric SYK, arXiv:1710.08184 [INSPIRE].

  53. A.M. García-García and J.J.M. Verbaarschot, Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N, Phys. Rev. D 96 (2017) 066012 [arXiv:1701.06593] [INSPIRE].

    ADS  Google Scholar 

  54. M. Rigol, Breakdown of thermalization in finite one-dimensional systems, Phys. Rev. Lett. 103 (2009) 100403 [arXiv:0904.3746].

    Article  ADS  Google Scholar 

  55. A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Virasoro Conformal Blocks and Thermality from Classical Background Fields, JHEP 11 (2015) 200 [arXiv:1501.05315] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  56. P. Gao, D.L. Jafferis and A. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].

    Article  ADS  Google Scholar 

  57. J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  58. A.J. Scott, Optimizing quantum process tomography with unitary 2-designs, J. Phys. A 41 (2008) 055308 [arXiv:0711.1017].

    ADS  MathSciNet  MATH  Google Scholar 

  59. F.G. S.L. Brandão, E. Crosson, M.B. Şahinoğlu and J. Bowen, Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains, arXiv:1710.04631 [INSPIRE].

  60. R. Gurau, The 1/N expansion of colored tensor models, Ann. Henri Poincaré 12 (2011) 829 [arXiv:1011.2726] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. E. Witten, An SYK-Like Model Without Disorder, arXiv:1610.09758 [INSPIRE].

  62. I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].

    ADS  Google Scholar 

  63. C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum Chaos and Holographic Tensor Models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. T.-C. Lu and T. Grover, Renyi Entropy of Chaotic Eigenstates, arXiv:1709.08784 [INSPIRE].

  65. N. Lashkari, A. Dymarsky and H. Liu, Eigenstate Thermalization Hypothesis in Conformal Field Theory, arXiv:1610.00302 [INSPIRE].

  66. P. Basu, D. Das, S. Datta and S. Pal, Thermality of eigenstates in conformal field theories, Phys. Rev. E 96 (2017) 022149 [arXiv:1705.03001] [INSPIRE].

    ADS  Google Scholar 

  67. A. Dymarsky, N. Lashkari and H. Liu, Subsystem ETH, Phys. Rev. E 97 (2018) 012140 [arXiv:1611.08764].

    ADS  Google Scholar 

  68. A. Dymarsky and H. Liu, Canonical Universality, arXiv:1702.07722 [INSPIRE].

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

  1. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California, 91125, U.S.A.

    Nicholas Hunter-Jones

  2. Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California, 91125, U.S.A.

    Junyu Liu

  3. Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada

    Yehao Zhou

  4. Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Yehao Zhou

Authors
  1. Nicholas Hunter-Jones
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junyu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yehao Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junyu Liu.

Additional information

ArXiv ePrint: 1710.03012

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hunter-Jones, N., Liu, J. & Zhou, Y. On thermalization in the SYK and supersymmetric SYK models. J. High Energ. Phys. 2018, 142 (2018). https://doi.org/10.1007/JHEP02(2018)142

Download citation

  • Received: 19 November 2017

  • Accepted: 07 February 2018

  • Published: 22 February 2018

  • DOI: https://doi.org/10.1007/JHEP02(2018)142

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • 2D Gravity
  • AdS-CFT Correspondence
  • Black Holes
  • Random Systems

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

Not affiliated

Springer Nature

© 2023 Springer Nature