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Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
by Charles Stahl, Rahul Nandkishore, Oliver Hart
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Oliver Hart · Rahul Nandkishore · Charles Stahl |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2304.04792v2 (pdf) |
| Date submitted: | April 25, 2023, 8:50 p.m. |
| Submitted by: | Charles Stahl |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present a set of generalized quantum loop models which provably exhibit topologically stable ergodicity breaking. These results hold for both periodic and open boundary conditions, and derive from a one-form symmetry (notably not being restricted to sectors of extremal one-form charge). We identify simple models in which this one-form symmetry can be emergent, giving rise to the aforementioned ergodicity breaking as an exponentially long-lived prethermal phenomenon. We unveil a web of dualities that connects these models, in certain limits, to models that have previously been discussed in the literature. We also identify nonlocal conserved quantities in such models that correspond to a pattern of system-spanning domain walls, and which are robust to the addition of arbitrary $k$-local perturbations.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2023-8-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.04792v2, delivered 2023-08-28, doi: 10.21468/SciPost.Report.7734
Strengths
1- Novel results on a timely topic 2- Very clearly written manuscript
Report
The results represent a novel mechanism allowing for a robust ergodicity breaking and are thus of strong interest. Moreover, the manuscript is well written and all results are presented clearly.
Minor comment: When reading the manuscript, I thought it might be useful to discuss whether the system is strongly or easily fragmented also in the main text.
In summary, this work contains novel results on a timely topic and the manuscript is very clearly written. I thus recommend publication in SciPost.
Report #2 by Anonymous (Referee 2) on 2023-8-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.04792v2, delivered 2023-08-09, doi: 10.21468/SciPost.Report.7627
Strengths
1- Clear presentation
2- Useful formatting and figures
3-Connects interesting and active topics (higher-form symmetries, ergodicity breaking)
Weaknesses
1- The novel parts of this work are mainly based on one specific model and it would be interesting to have a more generic/model-independent answer concerning the connection between ergodicity breaking and higher-form symmetries.
Report
The introduction highlights the general question, its challenges, the state-of-the-art, and places the current work into context.
Section 2 is a useful warm-up that reviews the one-dimensional pair-flip model. The authors argue that the fragmentation crucially depends on the restriction to nearest-neighbor-dynamics (a feature that they want to remedy).
Section 3 generalizes the pair-flip model to two dimensions. Using a 1-form symmetry the fragmentation is robust under generic local perturbations (topologically robust) and not "all or nothing" anymore. This section provides the main results of this work.
Section 4 provides further, not strictly necessary, details concerning the two-dimensional model: Other theories which arise as limits or via dualities and a discussion of a generalization to three dimensions (where 2-form symmetries are relevant).
The authors provide a conclusion and two appendices with further details.
This work opens the pathway for the exploration of ergodicity-breaking quantum dynamics that derive from higher-form symmetries and also provides a synergetic link between these different research areas. I am therefore happy to recommend this work for publication in SciPost Physics.
We thank the referee for the detailed and positive summary of our work, and for recommending publication.
The connection between ergodicity breaking and higher-form symmetries is actually rather subtle. For instance, in the class of square-lattice models we consider in this work, higher-form symmetry provides a powerful way of understanding the robust fragmentation. However, the same higher-form symmetry does not necessarily produce robust fragmentation on arbitrary lattices. Indeed, even formulating the symmetry on a lattice that is not bipartite is tricky. Resolving the question of how these models can be generalized to arbitrary lattices, and further clarifying the connections between higher-form symmetries and robust fragmentation, is an important and interesting problem for future work, but is beyond the scope of the current manuscript. We have added a paragraph to the conclusions discussing these subtleties.
Report #1 by Anonymous (Referee 1) on 2023-7-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.04792v2, delivered 2023-07-09, doi: 10.21468/SciPost.Report.7477
Report
We thank the referee for the positive assessment of our work and for recommending publication in SciPost Physics.
Author: Charles Stahl on 2023-12-28 [id 4214]
(in reply to Report 3 on 2023-08-28)We thank the referee for the favorable report and the recommendation for publication. To address the referee's one minor comment, we have added a new Appendix (Appendix C) discussing whether fragmentation in the model is weak or strong. To answer this question conclusively, we introduced a loop Monte Carlo algorithm for sampling from the constraint-satisfying subspace, which we used to show that the largest Krylov sector occupies almost all of Hilbert space in the thermodynamic limit, corresponding to weak fragmentation. We have also stated this result in the main text.