Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model

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1802.06796v2.pdf(715.26 KB)
First author draft
Date
2019-04-08
Authors
Schmitt, Markus
Sels, Dries
Kehrein, Stefan
Polkovnikov, Anatoli
Version
First author draft
OA Version
Citation
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
Abstract
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.
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