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On the intrinsic pinning and shape of charge-density waves in 1D Peierls systems

by O. Cépas, P. Quémerais

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Olivier Cépas
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-12-01
Date submitted: 2022-10-12 16:07
Submitted by: Cépas, Olivier
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of the electron-lattice models in the physical properties of Peierls systems? We study in details a nonlinear discrete model, introduced by Brazovskii, Dzyaloshinskii and Krichever. First, we recall its exact analytical solution at integrable points. It is a cnoidal wave, with a continuous envelope, which may slide over the lattice potential at no energy cost, following Fr\"ohlich's argument. Second, we show numerically that integrability-breaking terms modify some important physical properties. The envelope function may become discontinuous: electrons form stronger chemical bonds which are local dimers or oligomers. We show that an Aubry transition from the sliding phase to an insulating pinned phase occurs when the model is no longer integrable.

Author comments upon resubmission

Dear Editor,
We would like to resubmit our paper to SciPost Physics, after having made some major revisions of the text, following referees' advices. In particular, we have clarified ``what is new''. The paper considerably simplifies the solution of the integrable model and emphasizes its limitations. This is only one part of the paper and we are happy that both referees have acknowledged its pedagogical clarity. We stress that the whole study concerning the Aubry transition when the model is made nonintegrable is completely new in this context and is the main topic of the present paper. We thus hope that you will be in a position to accept the present paper without further review, given that the two referee reports are positive and we have included their suggestions.

The authors.

List of changes

Changes have been made, following the second referee's detailed corrections. They concern essentially the text, some formulations and the english: almost all the suggested changes have been kept (except for a few details such as ``the SSH model'' where ``the'' is kept, as explained in our reply to the referee). We have changed the second part of the abstract and part of the introduction (especially the last paragraph) to emphasize what is new and answer the referees' concerns. Appendix D has been clarified to answer the second referee's mathematical question.

Published as SciPost Phys. 14, 051 (2023)

Reports on this Submission

Anonymous Report 1 on 2022-10-19 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2204.00278v2, delivered 2022-10-18, doi: 10.21468/SciPost.Report.5924


1- Pedagogical explanations,
2- new phase diagram for an important family of Hamiltonians
3- innovant numerical investigations


1-Long article that can discourage reader
2- Ratio of new results which can be disappointing


The authors have addressed most of my concerns and taken into account most of my advices. I had misunderstood some explanations, which have become clear now. About the language, I only tried, in my first report, to help improving the manuscript; it is now satisfactory.
About the balance between afresh presentation of already established results and new numerical ones, I do not fully agree with the authors’ response. They claim that they “reformulate” previous results in a way that is both “original” and “new”. I agree with the originality of the presentation but “new” has a specific meaning, in article reports, which cannot apply here. I have actually not contested the pedagogical rewriting of previous works but only claimed that it is not obvious, reading the introduction, to discriminate the results which are new from others. The introduction has been improved and, if the editor agrees, I think this revised manuscript is worth being published.

Requested changes

I still claim that “whatever”, which is found several times in the manuscript as pronouns or adverb, must be used with a verb, as in “whatever this is”, when one writes in formal (elevated) English, even though the verb is often familiarly omitted.

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

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