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arXiv · 1910.04769

Quantum echo dynamics in the Sherrington-Kirkpatrick model

Silvia Pappalardi·Anatoli Polkovnikov·Alessandro Silva
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Abstract

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-$N$) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins $N$. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on $N$ and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

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Silvia Pappalardi, Anatoli Polkovnikov, Alessandro Silva. 2019-10-10. Quantum echo dynamics in the Sherrington-Kirkpatrick model. https://doi.org/10.21468/scipostphys.9.2.021

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