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Probing chaos in the spherical $p$-spin glass model

by Lorenzo Correale, Anatoli Polkovnikov, Marco Schirò, Alessandro Silva

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Submission summary

Authors (as registered SciPost users): Lorenzo Correale · Marco Schirò · Alessandro Silva
Submission information
Preprint Link: scipost_202309_00002v2  (pdf)
Date accepted: 2023-10-23
Date submitted: 2023-10-18 10:27
Submitted by: Correale, Lorenzo
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


We study the dynamics of a quantum $p$-spin glass model starting from initial states defined in microcanonical shells, in a classical regime. We compute different chaos estimators, such as the Lyapunov exponent and the Kolmogorov-Sinai entropy, and find a marked maximum as a function of the energy of the initial state. By studying the relaxation dynamics and the properties of the energy landscape we show that the maximal chaos emerges in correspondence with the fastest spin relaxation and the maximum complexity, thus suggesting a qualitative picture where chaos emerges as the trajectories are scattered over the exponentially many saddles of the underlying landscape. We also observe hints of ergodicity breaking at low energies, indicated by the correlation function and a maximum of the fidelity susceptibility.

Published as SciPost Phys. 15, 190 (2023)

Author comments upon resubmission

Dear Editor,

We thank the referees for their report.
We have made revisions based on the observations of Referee 2, as reported in the "List of changes".
We hope that with these changes the paper will be accepted for publication in Scipost.

List of changes

- We fixed all the typos noticed by the referee and clarified the definition of the vector $\mathbf{z}$ (now renamed as "$\mathbf{y}$").

- We improved the physical interpretation of the dynamics from the correlation functions, making a clear distinction between a real "ergodicity breaking" and "slow dynamics".

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