SciPost Submission Page
Quantum echo dynamics in the SherringtonKirkpatrick model
by Silvia Pappalardi, Anatoli Polkovnikov, Alessandro Silva
This is not the current version.
Submission summary
As Contributors:  Silvia Pappalardi · Anatoli Polkovnikov 
Arxiv Link:  https://arxiv.org/abs/1910.04769v2 (pdf) 
Date submitted:  20200217 01:00 
Submitted by:  Pappalardi, Silvia 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Understanding the footprints of chaos in quantummanybody systems has been under debate for a long time. In this work, we study the echo dynamics of the SherringtonKirkpatrick (SK) model with transverse field under effective time reversal, by investigating numerically its quantum and semiclassical dynamics. We explore how chaotic manybody 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 welldefined semiclassical (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 shortrange 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.
Ontology / Topics
See full Ontology or Topics database.Current status:
Author comments upon resubmission
List of changes
 We rewrote 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 semiclassical 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 rewrote 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 2020228 (Invited Report)
Strengths
1timely subject (OTOCs)
2cutting edge analytics and semiclassics
3Relevant results about timescales and possibility to observe exponetial growth of the OTOC.
Weaknesses
1OTOC considered is not the most widespread quantity
Report
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.
Silvia Pappalardi on 20200217
We would like to correct two typos present in the Reply to the report I:
Yours sincerly, Silvia Pappalardi, Anatoli Polkovnikov and Alessandro Silva