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

Thomas Scaffidi and Ehud Altman
Phys. Rev. B 100, 155128 – Published 15 October 2019

Abstract

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. 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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  • Received 12 January 2018
  • Revised 13 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.155128

©2019 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsNonlinear DynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Thomas Scaffidi1,2 and Ehud Altman1

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, Canada

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Issue

Vol. 100, Iss. 15 — 15 October 2019

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