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Phenomenological XXZ model for the competition between superconductivity and charge order in cuprates

by Giulia Venditti, Ilaria Maccari, Jose Lorenzana, Sergio Caprara

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Submission summary

Authors (as registered SciPost users): Giulia Venditti
Submission information
Preprint Link: scipost_202311_00001v1  (pdf)
Date accepted: 2023-11-10
Date submitted: 2023-11-01 13:39
Submitted by: Venditti, Giulia
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational, Phenomenological


We argue that there is a special doping point in the phase diagram of cuprates, such that the condensation of holes into a charge-ordered and a superconducting phase are degenerate in energy but with an energy barrier in between. We present Monte Carlo simulations of a phenomenological XXZ model of this problem without and with quenched disorder in two dimensions. While in the clean case, charge order and superconductivity are separated by a first-order line which is nearly independent of temperature, in the presence of quenched disorder, charge order is fragmented into domains separated by superconducting filaments reminiscent of the supersolid behaviour in $^4$He. Assuming weak interlayer couplings, the resulting phase diagram of the three-dimensional system is in good agreement with the experiments.

Author comments upon resubmission

Dear Editor,

We wish to resubmit our manuscript “Phenomenological XXZ model for the competition among superconductivity and charge order in cuprates”.

We want to thank the referees for their careful reading of the manuscript and for their useful comments and suggestions. We considered all the issues they raised and modified our manuscript accordingly. In particular, we changed the title from “Thermodynamic phase diagram of the competition among superconductivity and charge order in cuprates” according to their suggestions, and tuned the narrative so that the limitations and implicit assumptions we made are now clearer.
We provided a point-by-point reply to all their questions and critical remarks.

We hope that with the revisions made, the paper can now be accepted for publication in SciPost Physics.

We thank you for your consideration and look forward to hearing from you.
Sincerely yours,

On behalf of all authors,

Giulia Venditti and José Lorenzana

List of changes

List of changements:

- We changed the title to “Phenomenological XXZ model for the competition among superconductivity and charge order in cuprates” following the suggestion of the referees.
- Address of authors updated (Giulia Venditti and Ilaria Maccari)
- Abstract:
We refer to our model as a phenomenological XXZ model, following the suggestion of both referees. We refer to the “phase diagram of a three-dimensional system” (rather than “three-dimensional phase diagram”), following referee #2’s comment.
- 1. Introduction:
We further discussed the reasons why we believe that our model fits the phenomenology of underdoped cuprates and we elaborate more on the implicit assumption we made in building our model, as well as its limitations. We also indicated appropriate references for a more in-depth analysis.
- 3. Clean system
Following the suggestion of referee #2, we moved some discussions of the clean system in appendices, such as the details of the spinodal and first order transition points, and the phase diagram for B=2, keeping the explanation in the main text less verbose but still self-contained.
- 5. Phase diagram for a three-dimensional system
As pointed out by reviewer #2, we now refer to the “phase diagram of a three-dimensional system” instead of “the three-dimensional phase diagram”, which was indeed a bit confusing.
We also specify, in the last paragraph, the connection between our phenomenological parameters and the experiments.
- 6. Conclusions:
We specified again the limitations of our model. However, despite those limitations, we believe that the main physics of cuprates is well captured.
- We added Appendix A: Clean system, where we moved some details of Section 3. The Appendix is divided into subsections: A.1 Effect of the barrier potential B; A.2 B=0.2: mean-square magnetizations and susceptibilities; A.3 B=0.2: first order transition and spinodals; A.4 B=2 phase diagram.
- We updated the figures to be more readable and corrected the typos, as suggested by referee #2.

Published as SciPost Phys. 15, 230 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-11-1 (Invited Report)


No further remarks, the paper is ready for publication

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Anonymous Report 1 on 2023-11-1 (Invited Report)


The authors made sufficient revision of the paper following the suggestions of the referees. I have not futher objections to recommend the publication.

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  • originality: -
  • clarity: -
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