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

Sünderhauf, Christoph; Piroli, Lorenzo; Qi, Xiao-Liang; Schuch, Norbert; Cirac, J. Ignacio

doi:10.1007/jhep11(2019)038

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

Journal Article · Thu Nov 07 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep11(2019)038· OSTI ID:1803746

Sünderhauf, Christoph ^[1]; Piroli, Lorenzo ^[2]; Qi, Xiao-Liang ^[3]; Schuch, Norbert ^[2]; Cirac, J. Ignacio ^[2]

Max-Planck-Institut fur Quantenoptik, Garching (Germany); Munich Center for Quantum Science and Technology, Munchen (Germany); OSTI
Max-Planck-Institut fur Quantenoptik, Garching (Germany); Munich Center for Quantum Science and Technology, Munchen (Germany)
Stanford Univ., CA (United States). Stanford Inst. of Theoretical Physics (ITP); Stanford Univ., CA (United States). Dept. of Physics; Google, Mountain View, CA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0019380

OSTI ID:: 1803746

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 11 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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

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