Journal of High Energy Physics

, 2019:38 | Cite as

Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

  • Christoph SünderhaufEmail author
  • Lorenzo Piroli
  • Xiao-Liang Qi
  • Norbert Schuch
  • J. Ignacio Cirac
Open Access
Regular Article - Theoretical Physics


We consider the Brownian SYK model of N interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the Rényi-2 tripartite information of the unitary evolution operator, which were proposed as diagnostic tools for quantum chaos and scrambling, respectively. We show that their averaged dynamics can be studied as a quench problem at imaginary times in a model of N qudits, where the Hamiltonian displays site-permutational symmetry. By exploiting a description in terms of bosonic collective modes, we show that for the quantities of interest the dynamics takes place in a subspace of the effective Hilbert space whose dimension grows either linearly or quadratically with N , allowing us to perform numerically exact calculations up to N = 106. We analyze in detail the interesting features of the OTOCs, including their dependence on the chosen observables, and of the tripartite information. We observe explicitly the emergence of a scrambling time t ln N controlling the onset of both chaotic and scrambling behavior, after which we characterize the exponential decay of the quantities of interest to the corresponding Haar scrambled values.


Holography and condensed matter physics (AdS/CMT) Random Systems 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Christoph Sünderhauf
    • 1
    • 2
    Email author
  • Lorenzo Piroli
    • 1
    • 2
  • Xiao-Liang Qi
    • 3
    • 4
    • 5
  • Norbert Schuch
    • 1
    • 2
  • J. Ignacio Cirac
    • 1
    • 2
  1. 1.Max-Planck-Institut für QuantenoptikGarchingGermany
  2. 2.Munich Center for Quantum Science and TechnologyMünchenGermany
  3. 3.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.
  4. 4.Department of PhysicsStanford UniversityStanfordU.S.A.
  5. 5.GoogleMountain ViewU.S.A.

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