Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model
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Citation (published version)Markus Schmitt, Dries Sels, Stefan Kehrein, Anatoli Polkovnikov. 2019. "Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model." Physical review B: Condensed matter and materials physics, Volume 99, Issue 13, pp. 134301 - 134301 (10). https://doi.org/10.1103/PhysRevB.99.134301
The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question gained increased interest due to the proposal to probe chaotic dynamics and scrambling using out-of-time-order correlators. In this work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time reversal in a semiclassical approach. We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows to identify a Lyapunov exponent λ_L. In particular, we find that λ_L is twice the Lyapunov exponent of the semiclassical equations of motion. This behavior is attributed to the growth of an out-of-time-order double commutator that resembles an out-of-time-order correlator.