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Quantum echo dynamics in the Sherrington-Kirkpatrick model

by Silvia Pappalardi, Anatoli Polkovnikov, Alessandro Silva

Submission summary

As Contributors: Silvia Pappalardi · Anatoli Polkovnikov
Arxiv Link: (pdf)
Date accepted: 2020-07-31
Date submitted: 2020-07-28 09:07
Submitted by: Pappalardi, Silvia
Submitted to: SciPost Physics
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


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.

Ontology / Topics

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Quantum many-body systems

Published as SciPost Phys. 9, 021 (2020)

Author comments upon resubmission

List of changes

- We added the definition of OTOC in the introduction as a "multi-point and multi-time correlation functions which cannot be represented on a single Keldysh contour".
- We have specified *chaotic* when referring to the semi-classical limit as a condition for the exponential growth.
- We have corrected the typos in the references [70-71].
- We implemented the corrections to the Bopp formalism.

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