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Many-body chaos near a thermal phase transition

by Alexander Schuckert, Michael Knap

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Submission summary

Authors (as registered SciPost users): Michael Knap · Alexander Schuckert
Submission information
Preprint Link:  (pdf)
Date accepted: 2019-08-12
Date submitted: 2019-07-11 02:00
Submitted by: Schuckert, Alexander
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

Published as SciPost Phys. 7, 022 (2019)

List of changes

In response to Referee 1:
1) Re-evaluated data points in Figs.4+6 with a jackknife binning analysis and removed a couple of points around G_c to increase visibility. New paragraph in App. C explaining the error analysis. Slightly changed the interpretation of the results in 4.1 “Crossover near.”→”Signatures of a crossover near the phase transition” and “ordered phase”, also the corresponding discussion in the conclusions.
2) “Chaos spreads ballistically”->“OTOCs spread ballistically” everywhere
3) Typos indicated by the referee (see answer to report).
4) Chapter3: Removed fit parameters to Breit-Wigner in discussion of G=35.
5) Discussion of Ehrenfest time on p.10 changed
6) Changed second sentence of second paragraph in introduction and added Ref.8.
7) Now referring to new Ref.68 in chapter 4.3

In response to referee 2:
8) Changed discussion of results of fluctuations in chapter 4.3 and corresponding section in conclusions.

Reports on this Submission

Anonymous Report 1 on 2019-8-7 (Invited Report)


The authors have resolved all the issues I had raised in my previous report and revised the manuscript accordingly. The paper can now be published without further changes.

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