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Quantum quenches and thermalization in SYK models

  • Ritabrata Bhattacharya
  • Dileep P. Jatkar
  • Nilakash SorokhaibamEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We study non-equilibrium dynamics in SYK models using quantum quench. We consider models with two, four, and higher fermion interactions (q = 2, 4, and higher) and use two different types of quench protocol, which we call step and bump quenches. We analyse evolution of fermion two-point functions without long time averaging. We observe that in q = 2 theory the two-point functions do not thermalize. We find thermalization in q = 4 and higher theories without long time averaging. We calculate two different exponents of which one is equal to the coupling and the other is proportional to the final temperature. This result is more robust than thermalization obtained from long time averaging as proposed by the eigenstate thermalization hypothesis(ETH). Thermalization achieved without long time averaging is more akin to mixing than ergodicity.

Keywords

AdS-CFT Correspondence Field Theories in Lower Dimensions 1/N Expansion Holography and condensed matter physics (AdS/CMT) 

Notes

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.

References

  1. [1]
    C. Gogolin and J. Eisert, Equilibration, thermalisation and the emergence of statistical mechanics in closed quantum systems, Rept. Prog. Phys. 79 (2016) 056001 [arXiv:1503.07538] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    J.H. Traschen and R.H. Brandenberger, Particle Production During Out-of-equilibrium Phase Transitions, Phys. Rev. D 42 (1990) 2491 [INSPIRE].ADSGoogle Scholar
  3. [3]
    M. Cramer, C.M. Dawson, J. Eisert and T.J. Osborne, Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems, Phys. Rev. Lett. 100 (2008) 030602 [cond-mat/0703314] [INSPIRE].
  4. [4]
    A.Y. Kitaev, A simple model of quantum holography, talk at Entanglement in strongly-correlated quantum matter, KITP, University of California, Santa Barbara (2015).Google Scholar
  5. [5]
    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].CrossRefGoogle Scholar
  6. [6]
    J. Erdmenger, M. Flory, M.-N. Newrzella, M. Strydom and J.M.S. Wu, Quantum Quenches in a Holographic Kondo Model, JHEP 04 (2017) 045 [arXiv:1612.06860] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. Cardy, Thermalization and Revivals after a Quantum Quench in Conformal Field Theory, Phys. Rev. Lett. 112 (2014) 220401 [arXiv:1403.3040] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Polkovnikov, K. Sengupta, A. Silva and M. Vengalattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83 (2011) 863 [arXiv:1007.5331] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    P. Calabrese and J. Cardy, Quantum Quenches in Extended Systems, J. Stat. Mech. 0706 (2007) P06008 [arXiv:0704.1880] [INSPIRE].MathSciNetGoogle Scholar
  10. [10]
    G. Mandal, R. Sinha and N. Sorokhaibam, Thermalization with chemical potentials and higher spin black holes, JHEP 08 (2015) 013 [arXiv:1501.04580] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    S.R. Das, D.A. Galante and R.C. Myers, Smooth and fast versus instantaneous quenches in quantum field theory, JHEP 08 (2015) 073 [arXiv:1505.05224] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    A. Goel, H.T. Lam, G.J. Turiaci and H. Verlinde, Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK, JHEP 02 (2019) 156 [arXiv:1807.03916] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    N. Hunter-Jones, J. Liu and Y. Zhou, On thermalization in the SYK and supersymmetric SYK models, JHEP 02 (2018) 142 [arXiv:1710.03012] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    G. Mandal, S. Paranjape and N. Sorokhaibam, Thermalization in 2D critical quench and UV/IR mixing, JHEP 01 (2018) 027 [arXiv:1512.02187] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    J.M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991) 2046.ADSCrossRefGoogle Scholar
  18. [18]
    M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    D. Fioretto and G. Mussardo, Quantum Quenches in Integrable Field Theories, New J. Phys. 12 (2010) 055015 [arXiv:0911.3345] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    D. Das, S.R. Das, D.A. Galante, R.C. Myers and K. Sengupta, An exactly solvable quench protocol for integrable spin models, JHEP 11 (2017) 157 [arXiv:1706.02322] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  21. [21]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    E. Witten, An SYK-Like Model Without Disorder, arXiv:1610.09758 [INSPIRE].
  23. [23]
    G. Mandal, P. Nayak and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, JHEP 11 (2017) 046 [arXiv:1702.04266] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    J. Sonner and M. Vielma, Eigenstate thermalization in the Sachdev-Ye-Kitaev model, JHEP 11 (2017) 149 [arXiv:1707.08013] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    M. Haque and P. McClarty, Eigenstate Thermalization Scaling in Majorana Clusters: from Integrable to Chaotic SYK Models, arXiv:1711.02360 [INSPIRE].
  26. [26]
    D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M. Berkooz, P. Narayan, M. Rozali and J. Simón, Higher Dimensional Generalizations of the SYK Model, JHEP 01 (2017) 138 [arXiv:1610.02422] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    I.R. Klebanov and G. Tarnopolsky, On Large N Limit of Symmetric Traceless Tensor Models, JHEP 10 (2017) 037 [arXiv:1706.00839] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS 2 gravity, arXiv:1707.02325 [INSPIRE].
  31. [31]
    P. Narayan and J. Yoon, SYK-like Tensor Models on the Lattice, JHEP 08 (2017) 083 [arXiv:1705.01554] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    S.R. Das, A. Jevicki and K. Suzuki, Three Dimensional View of the SYK/AdS Duality, JHEP 09 (2017) 017 [arXiv:1704.07208] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    G. Turiaci and H. Verlinde, Towards a 2d QFT Analog of the SYK Model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    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].ADSMathSciNetGoogle Scholar
  35. [35]
    C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum Chaos and Holographic Tensor Models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    C. Krishnan, K.V. Pavan Kumar and D. Rosa, Contrasting SYK-like Models, JHEP 01 (2018) 064 [arXiv:1709.06498] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  37. [37]
    N. Callebaut and H. Verlinde, Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM, JHEP 05 (2019) 045 [arXiv:1808.05583] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    A. Gaikwad, L.K. Joshi, G. Mandal and S.R. Wadia, Holographic dual to charged SYK from 3D Gravity and Chern-Simons, arXiv:1802.07746 [INSPIRE].
  39. [39]
    S. Choudhury, A. Dey, I. Halder, L. Janagal, S. Minwalla and R. Poojary, Notes on melonic O(N )q−1 tensor models, JHEP 06 (2018) 094 [arXiv:1707.09352] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Space-Time in the SYK Model, JHEP 07 (2018) 184 [arXiv:1712.02725] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    K. Bulycheva, I.R. Klebanov, A. Milekhin and G. Tarnopolsky, Spectra of Operators in Large N Tensor Models, Phys. Rev. D 97 (2018) 026016 [arXiv:1707.09347] [INSPIRE].ADSMathSciNetGoogle Scholar
  42. [42]
    P. Narayan and J. Yoon, Supersymmetric SYK Model with Global Symmetry, JHEP 08 (2018) 159 [arXiv:1712.02647] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    I.R. Klebanov, F. Popov and G. Tarnopolsky, TASI Lectures on Large N Tensor Models, PoS(TASI2017) 004 (2018) [arXiv:1808.09434] [INSPIRE].Google Scholar
  44. [44]
    A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Three Dimensional View of Arbitrary q SYK models, JHEP 02 (2018) 162 [arXiv:1711.09839] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  47. [47]
    K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    D. Roychowdhury, q SYK models with Yang-Baxter deformations, arXiv:1810.09404 [INSPIRE].
  49. [49]
    P. Calabrese and J.L. Cardy, Time-dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96 (2006) 136801 [cond-mat/0601225] [INSPIRE].
  50. [50]
    S. Ziraldo et al., Thermalization and relaxation after a quantum quench in disordered Hamiltonians, Ph.D. Thesis, SISSA (2013).Google Scholar
  51. [51]
    P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories, J. Stat. Mech. 1606 (2016) 064003 [arXiv:1603.02889] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  52. [52]
    M. Greiner, O. Mandel, T.W. Hänsch and I. Bloch, Collapse and revival of the matter wave field of a Bose-Einstein condensate, Nature 419 (2002) 51.ADSCrossRefGoogle Scholar
  53. [53]
    T. Kinoshita, T. Wenger and D.S. Weiss, A quantum Newtons cradle, Nature 440 (2006) 900.ADSCrossRefGoogle Scholar
  54. [54]
    S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    E. Caceres, A. Kundu, J.F. Pedraza and D.-L. Yang, Weak Field Collapse in AdS: Introducing a Charge Density, JHEP 06 (2015) 111 [arXiv:1411.1744] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
  57. [57]
    M. Babadi, E. Demler and M. Knap, Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions, Phys. Rev. X 5 (2015) 041005 [arXiv:1504.05956] [INSPIRE].CrossRefGoogle Scholar
  58. [58]
    J. Maciejko, An introduction to nonequilibrium many-body theory, Springer (2007).Google Scholar
  59. [59]
    J.M. Magan, Random free fermions: An analytical example of eigenstate thermalization, Phys. Rev. Lett. 116 (2016) 030401 [arXiv:1508.05339] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  60. [60]
    M. Rigol and M. Srednicki, Alternatives to eigenstate thermalization, Phys. Rev. Lett. 108 (2012) 110601.ADSCrossRefGoogle Scholar
  61. [61]
    V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].ADSGoogle Scholar
  62. [62]
    J. Cardy, Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories, SciPost Phys. 3 (2017) 011 [arXiv:1706.01568] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    S. Paranjape and N. Sorokhaibam, Exact Growth of Entanglement and Dynamical Phase Transition in Global Fermionic Quench, arXiv:1609.02926 [INSPIRE].
  64. [64]
    A. Kamenev, Field theory of non-equilibrium systems, Cambridge University Press (2011).Google Scholar
  65. [65]
    A.M. Garcıa-García, B. Loureiro, A. Romero-Bermúdez and M. Tezuka, Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model, Phys. Rev. Lett. 120 (2018) 241603 [arXiv:1707.02197] [INSPIRE]
  66. [66]
    H. Ebrahim and M. Headrick, Instantaneous Thermalization in Holographic Plasmas, arXiv:1010.5443 [INSPIRE].
  67. [67]
    V. Keranen and P. Kleinert, Non-equilibrium scalar two point functions in AdS/CFT, JHEP 04 (2015) 119 [arXiv:1412.2806] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  68. [68]
    J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
  69. [69]
    R. Balescu, Equilibrium and nonequilibrium statistical mechanics, New York, NY, Wiley (1975).zbMATHGoogle Scholar

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Harish-Chandra Research InstituteHomi Bhabha National InstituteAllahabadIndia

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