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Quantum echo dynamics in the Sherrington-Kirkpatrick model
by Silvia Pappalardi, Anatoli Polkovnikov, Alessandro Silva
This is not the current version.
|As Contributors:||Silvia Pappalardi · Anatoli Polkovnikov|
|Arxiv Link:||https://arxiv.org/abs/1910.04769v2 (pdf)|
|Date submitted:||2020-02-17 01:00|
|Submitted by:||Pappalardi, Silvia|
|Submitted to:||SciPost Physics|
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, by investigating 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 it experimentally.
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Author comments upon resubmission
List of changes
- We re-wrote the introduction in a more cohesive manner.
- We added a small comparison between the SK and SYK models.
- We added a new appendix containing the derivation of the semi-classical limit of the echo observable and the square commutator.
- We added a new appendix containing the derivation of TWA and its validity for the SK model.
- We re-wrote the introduction to TWA in Section 5.
- We changed the caption of the pictures and added ordinate labels when missing. In Fig.4, we added an exponential function to guide the reader's eyes to the thermodynamic limit.
- We improved the discussion of the numerical findings in Section 6.
- Updated bibliography.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2020-2-28 (Invited Report)
1-timely subject (OTOCs)
2-cutting edge analytics and semiclassics
3-Relevant results about time-scales and possibility to observe exponetial growth of the OTOC.
1-OTOC considered is not the most widespread quantity
The authors have answered the concerns of the referees rather carefully and I think the manuscript in the present form is a significant contribution to the subject of characterizing chaos in complex quantum systems. I recommend publication.