Chaos in a classical limit of the Sachdev-Ye-Kitaev model

Scaffidi, Thomas; Altman, Ehud

doi:10.1103/physrevb.100.155128

Title: Chaos in a classical limit of the Sachdev-Ye-Kitaev model

Journal Article · Tue Oct 15 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.100.155128· OSTI ID:1803759

Scaffidi, Thomas ^[1]; Altman, Ehud ^[2]

Univ. of California, Berkeley, CA (United States)
Univ. of Toronto, ON (Canada)

We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on temperature, with a slope that is parametrically different than in the quantum case: It is proportional to N/S. The classical dynamics can be understood as the rotation of an N-dimensional body with a random inertia tensor, corresponding to the random couplings of the SYK Hamiltonian. This allows us to find an extensive number of fixed points, corresponding to the body's principal axes of rotation. Finally, the thermodynamics is mapped to the p-spin model with p = 2, which exhibits a spin glass phase at low temperature whose presence does not preclude the existence of chaos.

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Research Organization:: Univ. of California, Oakland, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: Gordon and Betty Moore Foundation; European Research Council (ERC); USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0019380; AC02-05CH11231; UQUAM

OSTI ID:: 1803759

Journal Information:: Physical Review. B, Vol. 100, Issue 15; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (43)

The classical limit of quantum partition functions Simon, Barry Communications in Mathematical Physics, Vol. 71, Issue 3 https://doi.org/10.1007/BF01197294	journal	October 1980
Variation of Lyapunov exponents on a strange attractor Abarbanel, H. D. I.; Brown, R.; Kennel, M. B. Journal of Nonlinear Science, Vol. 1, Issue 2 https://doi.org/10.1007/BF01209065	journal	June 1991
Review of the k-Body Embedded Ensembles of Gaussian Random Matrices Benet, L.; Weidenmueller, H. A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0207656	text	January 2002
Chaos and Quantum Thermalization Srednicki, Mark arXiv https://doi.org/10.48550/arxiv.cond-mat/9403051	text	January 1994
Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory Andreev, A. V.; Agam, O.; Simons, B. D. arXiv https://doi.org/10.48550/arxiv.cond-mat/9601001	text	January 1996
Sachdev–Ye–Kitaev model as Liouville quantum mechanics Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex Nuclear Physics B, Vol. 911 https://doi.org/10.1016/j.nuclphysb.2016.08.002	journal	October 2016
Power-law out of time order correlation functions in the SYK model Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex Nuclear Physics B, Vol. 921 https://doi.org/10.1016/j.nuclphysb.2017.06.012	journal	August 2017
The Spectrum in the Sachdev-Ye-Kitaev Model Polchinski, Joseph; Rosenhaus, Vladimir arXiv https://doi.org/10.48550/arxiv.1601.06768	text	January 2016
Semiclassical approach to Dynamics of Interacting Fermions Davidson, Shainen M.; Sels, Dries; Polkovnikov, Anatoli arXiv https://doi.org/10.48550/arxiv.1604.08664	text	January 2016
Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass Georges, A.; Parcollet, O.; Sachdev, S. arXiv https://doi.org/10.48550/arxiv.cond-mat/0009388	text	January 2000
Systematic evolution of temperature-dependent resistivity in ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$ Takagi, H.; Batlogg, B.; Kao, H. L. Physical Review Letters, Vol. 69, Issue 20 https://doi.org/10.1103/PhysRevLett.69.2975	journal	November 1992
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)106	journal	August 2016
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet Sachdev, Subir; Ye, Jinwu arXiv https://doi.org/10.48550/arxiv.cond-mat/9212030	text	January 1992
Geometric approach to Hamiltonian dynamics and statistical mechanics Casetti, Lapo; Pettini, Marco; Cohen, E. G. D. Physics Reports, Vol. 337, Issue 3 https://doi.org/10.1016/S0370-1573(00)00069-7	journal	October 2000
Remarks on the Sachdev-Ye-Kitaev model Maldacena, Juan; Stanford, Douglas Physical Review D, Vol. 94, Issue 10 https://doi.org/10.1103/PhysRevD.94.106002	journal	November 2016
The spectrum in the Sachdev-Ye-Kitaev model Polchinski, Joseph; Rosenhaus, Vladimir Journal of High Energy Physics, Vol. 2016, Issue 4 https://doi.org/10.1007/JHEP04(2016)001	journal	April 2016
Full dynamical solution for a spherical spin-glass model Cugliandolo, L. F.; Dean, D. S. Journal of Physics A: Mathematical and General, Vol. 28, Issue 15 https://doi.org/10.1088/0305-4470/28/15/003	journal	August 1995
Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits Arnold, Vladimir Annales de l’institut Fourier, Vol. 16, Issue 1 https://doi.org/10.5802/aif.233	journal	January 1966
Theory of universal incoherent metallic transport Hartnoll, Sean A. arXiv https://doi.org/10.48550/arxiv.1405.3651	text	January 2014
Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model Cugliandolo, Leticia F.; Lozano, Gustavo S.; Nessi, Nicolas arXiv https://doi.org/10.48550/arxiv.1712.07688	text	January 2017
Gapless spin-fluid ground state in a random quantum Heisenberg magnet Sachdev, Subir; Ye, Jinwu Physical Review Letters, Vol. 70, Issue 21 https://doi.org/10.1103/PhysRevLett.70.3339	journal	May 1993
Thermal diffusivity and chaos in metals without quasiparticles Blake, Mike; Davison, Richard A.; Sachdev, Subir Physical Review D, Vol. 96, Issue 10 https://doi.org/10.1103/PhysRevD.96.106008	journal	November 2017
Theory of universal incoherent metallic transport Hartnoll, Sean A. Nature Physics, Vol. 11, Issue 1 https://doi.org/10.1038/nphys3174	journal	December 2014
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas arXiv https://doi.org/10.48550/arxiv.1503.01409	text	January 2015
Quantum fluctuations of a nearly critical Heisenberg spin glass Georges, A.; Parcollet, O.; Sachdev, S. Physical Review B, Vol. 63, Issue 13 https://doi.org/10.1103/PhysRevB.63.134406	journal	March 2001
Geometric approach to Hamiltonian dynamics and statistical mechanics Casetti, Lapo; Pettini, Marco; Cohen, E. G. D. arXiv https://doi.org/10.48550/arxiv.cond-mat/9912092	text	January 1999
Superconductivity in Bad Metals Emery, V. J.; Kivelson, S. A. Physical Review Letters, Vol. 74, Issue 16 https://doi.org/10.1103/PhysRevLett.74.3253	journal	April 1995
Out-of-time-order operators and the butterfly effect Cotler, Jordan S.; Ding, Dawei; Penington, Geoffrey R. Annals of Physics, Vol. 396 https://doi.org/10.1016/j.aop.2018.07.020	journal	September 2018
Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang SciPost Physics, Vol. 2, Issue 3 https://doi.org/10.21468/SciPostPhys.2.3.018	journal	January 2017
Thermal diffusivity and chaos in metals without quasiparticles Blake, Mike; Davison, Richard A.; Sachdev, Subir arXiv https://doi.org/10.48550/arxiv.1705.07896	text	January 2017
Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model Cugliandolo, Leticia F.; Lozano, Gustavo S.; Nessi, Nicolás Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, Issue 6 https://doi.org/10.1088/1742-5468/aac2fe	journal	June 2018
Review of the k -body embedded ensembles of Gaussian random matrices Benet, L.; Weidenm ller, H. A. Journal of Physics A: Mathematical and General, Vol. 36, Issue 12 https://doi.org/10.1088/0305-4470/36/12/340	journal	March 2003
Semiclassical approach to dynamics of interacting fermions Davidson, Shainen M.; Sels, Dries; Polkovnikov, Anatoli Annals of Physics, Vol. 384 https://doi.org/10.1016/j.aop.2017.07.003	journal	September 2017
Spherical Model of a Spin-Glass Kosterlitz, J. M.; Thouless, D. J.; Jones, Raymund C. Physical Review Letters, Vol. 36, Issue 20 https://doi.org/10.1103/PhysRevLett.36.1217	journal	May 1976
Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models Klebanov, Igor R.; Tarnopolsky, Grigory Physical Review D, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevD.95.046004	journal	February 2017
Strongly Correlated Metal Built from Sachdev-Ye-Kitaev Models Song, Xue-Yang; Jian, Chao-Ming; Balents, Leon Physical Review Letters, Vol. 119, Issue 21 https://doi.org/10.1103/PhysRevLett.119.216601	journal	November 2017
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Non-Fermi-liquid regime of a doped Mott insulator Parcollet, Olivier; Georges, Antoine Physical Review B, Vol. 59, Issue 8 https://doi.org/10.1103/PhysRevB.59.5341	journal	February 1999
Universal Charge Diffusion and the Butterfly Effect in Holographic Theories Blake, Mike Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.091601	journal	August 2016
Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory Andreev, A. V.; Agam, O.; Simons, B. D. Physical Review Letters, Vol. 76, Issue 21 https://doi.org/10.1103/PhysRevLett.76.3947	journal	May 1996
Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1702.08462	text	January 2017
Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model Schmitt, Markus; Sels, Dries; Kehrein, Stefan Physical Review B, Vol. 99, Issue 13 https://doi.org/10.1103/PhysRevB.99.134301	journal	April 2019
Geometry and non-adiabatic response in quantum and classical systems Kolodrubetz, Michael; Sels, Dries; Mehta, Pankaj Physics Reports, Vol. 697 https://doi.org/10.1016/j.physrep.2017.07.001	journal	June 2017

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