SciPost Submission Page
Topology-induced symmetry breaking demonstrated in antiferromagnetic magnons on a Möbius strip
by Kuangyin Deng, Ran Cheng
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Kuangyin Deng |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202505_00005v1 (pdf) |
| Date submitted: | May 3, 2025, 12:58 a.m. |
| Submitted by: | Kuangyin Deng |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We propose a mechanism of topology-induced symmetry breaking, where certain local symmetry preserved by the Hamiltonian is explicitly broken in the eigenmodes of excitation due to nontrivial real-space topology. We demonstrate this phenomenon by studying magnonic excitations on a Möbius strip comprising of two antiferromagnetically coupled spin chains. Even with a simple Hamiltonian respecting local rotational symmetry and all local curvature effects ignored, magnons exhibit linear polarization of the Néel vector devoid of chirality, forming two non-degenerate branches that cannot be smoothly connected to or be globally decomposed by the circularly-polarized magnons. Correspondingly, one branch undergoes a spectral shift and only admits standing waves of half-integer wavelength, whereas the other only affords standing waves of integer wavelength. Under the Möbius boundary condition, we further identify an exotic phase hosting spontaneous antiferromagnetic order whilst all exchange couplings are ferromagnetic. The suppression of chirality in the order parameter dynamics, hence the pattern of standing waves, can be generalized to other elementary excitations on non-orientable surfaces. Our findings showcase the profound influence of real-space topology on the physical nature of not just the ground state but also the quasiparticles.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #2 by Daniel Cabra (Referee 2) on 2025-7-13 (Invited Report)
- Cite as: Daniel Cabra, Report on arXiv:scipost_202505_00005v1, delivered 2025-07-13, doi: 10.21468/SciPost.Report.11561
Report
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Anonymous (Referee 1) on 2025-6-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202505_00005v1, delivered 2025-06-29, doi: 10.21468/SciPost.Report.11478
Strengths
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The paper reports on an interesting observation, viz. the topology-induced breaking of symmetry in the excitation spectrum of a magnetic model on a Möbius strip that occurs despite the lack of such symmetry-breaking in the ground state.
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The paper is very clearly written, with ample and helpful interpretation of the results obtained.
Weaknesses
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The paper has an 'outlook' section, but no 'conclusion' section where the results are summarised. Such a conclusion section is required by SciPost Physics general acceptance criterion 4.
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There are occasional errors in the grammar, e.g. "topological protected" on page 7.
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The abbreviative convention in which a second sentence is included in parentheses within a first, rather than written separately, is overused, sometimes to the point of impairing meaning. See, for example, "$q^1_{\alpha(\beta)} < q^2_{\alpha(\beta)},$ leading to elongated trajectories in the $y$-direction ($x$-direction) for the $\alpha$ ($\beta$) modes" on page 7. This technique makes things easier for the writer, but harder for the reader; I recommend avoiding its use altogether.
Report
The general acceptance criteria are also met, with one exception, number 4: the paper does not currently have "a clear conclusion summarizing the results". However, I don't think it would be difficult for the authors to add one.
I therefore recommend publication, subject to the requirement that a conclusion be written, and the recommendation that weaknesses 2 and 3 in the above list are also remedied.
Requested changes
- Add a conclusion.
- Correct grammatical errors.
- Remove use of the "We see A (B) in case C (D)" device.
Recommendation
Publish (meets expectations and criteria for this Journal)
Reply to Referee 1
We thank you for evaluating our manuscript, which we believe now meets the SciPost Physics criteria. Below, we address your concerns.
Referee 1: The paper has an "outlook" section, but no "conclusion" section where the results are summarised. Such a conclusion section is required by SciPost Physics general acceptance criterion 4.
Our response: Now we have added the conclusion into the last section "Conclusion and Outlook".
Referee 1: There are occasional errors in the grammar, e.g. "topological protected" on page 7.
Our response: We have corrected the errors and typos in the manuscript shown with colored words.
Referee 1: The abbreviative convention in which a second sentence is included in parentheses within a first, rather than written separately, is overused, sometimes to the point of impairing meaning. See, for example, "$q_{\alpha(\beta)}^1$ < $q_{\alpha(\beta)}^2$, leading to elongated trajectories in the y-direction (x-direction) for the
$\alpha\,(\beta)$ modes" on page 7. This technique makes things easier for the writer, but harder for the reader; I recommend avoiding its use altogether.
Our response: The original idea was to use this abbreviative convention to prevent the redundancy. Following your suggestion, now we have significantly reduced the use of this form as much as we can for easier reading. Some of the sentences are rewritten.
Author: Kuangyin Deng on 2025-07-23 [id 5667]
(in reply to Report 2 by Daniel Cabra on 2025-07-13)Please see the response in the attached file.
Attachment:
SciPost_reply_to_referee_2.pdf