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Exact Mazur bounds in the pair-flip model and beyond
by Oliver Hart
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Submission summary
| Authors (as registered SciPost users): | Oliver Hart |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2308.00738v2 (pdf) |
| Date accepted: | 2024-06-03 |
| Date submitted: | 2024-04-05 07:29 |
| Submitted by: | Hart, Oliver |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general $p$-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as $1/\sqrt{L}$, rather than $1/L$, as had previously been thought. This result implies that the nontrivial conserved operators implied by $p$-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.
Author comments upon resubmission
Thank you for arranging the review of this manuscript. Given the recommendation of the second referee, I am resubmitting the manuscript for consideration in SciPost Physics Core. I have left a detailed response to each referee on the submission page, which thoroughly addresses their comments and criticisms. The manuscript has been modified accordingly and I am confident that it will now be judged suitable for publication.
Sincerely,
Oliver Hart
List of changes
1. Added a new section (4.1.4) describing a boundary-localized operator that is sufficient to establish asymptotically nonzero autocorrelation functions at the edges of the system.
2. Included numerical data in Figures 4 and 6 to verify the exact analytical manipulations presented in the manuscript.
3. Removed all instances of the phrase "nonlocal conserved quantities" to avoid confusion.
4. Improved referencing throughout the manuscript.
5. Highlighted the existence of a large length scale in the problem, which provides some intuition for the crossover observed in Figure 6.
Published as SciPost Phys. Core 7, 040 (2024)
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2024-5-11 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2308.00738v2, delivered 2024-05-11, doi: 10.21468/SciPost.Report.9037
Report
The Author has sufficiently answered all of the remarks/criticisms of the referees and has made the requested changes. I thank them for providing clear and concise explanations in their response to my concerns. I believe the manuscript is now perfectly suitable for publication in SciPost Physics Core, as resubmitted.
A small remark: regarding the model in reference [22], there in fact exists additional literature that could be of interest to the Author, independently of the current submission. It seems the model can be tackled using Bethe ansatz [J. Phys. A: Math. Gen. 24 L549 (1991), SciPost Phys. Core 4, 010 (2021), Phys. Rev. E 104, 044106 (2021)] and its fragmentation has been linked to special conserved quantities already in a classical setting [J. Stat. Phys. 86, 1237 (1997)].
Recommendation
Publish (meets expectations and criteria for this Journal)