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Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model

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Schmitt,  Markus
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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1802.06796.pdf
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Citation

Schmitt, M., Sels, D., Kehrein, S., & Polkovnikov, A. (2019). Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model. Physical Review B, 99(13): 134301. doi:10.1103/PhysRevB.99.134301.


Cite as: https://hdl.handle.net/21.11116/0000-0003-D121-B
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 has 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 using the truncated Wigner approximation, which accounts for nonvanishing quantum fluctuations that are essential for the dynamics. We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows us to identify a Lyapunov exponent lambda(L). In particular, we find that lambda(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.