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A simple theory for quantum quenches in the ANNNI model

by Jacob H. Robertson, Riccardo Senese, Fabian H. L. Essler

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Submission summary

Authors (as registered SciPost users): Fabian Essler · Jacob Robertson
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-05-24
Date submitted: 2023-04-04 13:19
Submitted by: Robertson, Jacob
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


In a recent numerical study by Haldar et al. (Phys. Rev. X 11, 031062) it was shown that signatures of proximate quantum critical points can be observed at early and intermediate times after certain quantum quenches. Said work focused mainly on the case of the axial next-nearest neighbour Ising (ANNNI) model. Here we construct a simple time-dependent mean-field theory that allows us to obtain a quantitatively accurate description of these quenches at short times, which for reasons we explain remains a fair approximation at late times (with some caveats). Our approach provides a simple framework for understanding the reported numerical results as well as fundamental limitations on detecting quantum critical points through quench dynamics. We moreover explain the origin of the peculiar oscillatory behaviour seen in various observables as arising from the formation of a long-lived bound state.

Published as SciPost Phys. 15, 032 (2023)

Author comments upon resubmission

Dear Editor and referees,

We thank you for your work in reviewing the manuscript and suggesting changes to improve it. We have made several improvements in line with these suggestions and have written a detailed reply to Referee 2 thanking them for useful suggestions that we have adopted and explaining why some of their further suggestions are beyond the scope of our work.

Kind regards,
The authors

List of changes

• Changed referencing in abstract to be able to stand alone in a repository.
• Replaced the phrase “surprisingly good approximation” with “fair approximation” in the abstract.
• Added several references ([17],[25],[41],[42],[57]) that were missing from the previous version.
• Added a sentence below Eq (1) to justify working in only the Neveu-Schwarz sector.
• Above Fig. 1 added a sentence to explicitly state that we restrict our analysis to the regime Ref. 1 investigates.
• Added arrows to Fig. 1 to indicate the quenches considered.
• Added a sentence of clarification below Eq. (3) about why the mean-field theory should be expected to work well in the regime studied and a further sentence explaining why it would be expected to perform poorly for other regions of the phase diagram.
• Added a note below Eq. (13) that J_{\rm Eff} and \Delta_{\rm Eff} are not necessarily equal.
• Made capitalisation consistent with ‘Eff’ subscripts.
• Added a new discussion to Sec. 4 below Eq. (24) that clarifies the limitations of SCTDMFT and explains why here it can provide a reasonable approximation, in line with the request made by Reviewer 2.
• Reworded the second bullet point in Sec. 4.1 to be clearer.
• Added citations above Eq. (33) for the quasiparticle description used.
• Added two sentences above Fig. 13 clarifying that the parameters used correspond to those in Fig. 10(a) and that the bound state signature is still present in single time observables, so the lack of a bound state in Fig. 13 is surprising.
• In the conclusions changed ‘surprisingly accurate’ to ‘fairly accurate’.
• Added a sentence in the conclusions to stress that the quench can only detect quantum critical behaviour if the energy density is below a cutoff scale, in line with the comments of Sec. 3.1.
• Altered the final sentence of the conclusions to be clear that the mean-field theory captures the bound state in equal time observables but not in the two-time quantity considered in Fig. 13.

Reports on this Submission

Anonymous Report 2 on 2023-4-28 (Invited Report)


The revised version has addressed my main concerns and especially clarified the limitations of mean field analysis at later times. I recommend that the paper is now accepted.

  • validity: high
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2023-4-18 (Invited Report)


As I have indicated in my previous report, I recommend this manuscript for publication.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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