# Quantum echo dynamics in the Sherrington-Kirkpatrick model

### Submission summary

 As Contributors: Silvia Pappalardi Arxiv Link: https://arxiv.org/abs/1910.04769v1 Date submitted: 2019-10-15 Submitted by: Pappalardi, Silvia Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approach: Theoretical

### 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 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 them experimentally.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1910.04769v1 on 15 October 2019