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19 April 2024 |
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Article overview
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Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information | | Christoph Sünderhauf
; Lorenzo Piroli
; Xiao-Liang Qi
; Norbert Schuch
; J. Ignacio Cirac
; | | Date: |
2 Aug 2019 | | Abstract: | 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
R’enyi-$2$ 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 $N = 10^6$. 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 $t^astsim ln N$ 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. | | Source: | arXiv, 1908.0775 | | Services: | Forum | Review | PDF | Favorites | |
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