SciPost Submission Page
Defect Networks for Topological Phases Protected By Modulated Symmetries
by Daniel Bulmash
Submission summary
| Authors (as registered SciPost users): | Daniel Bulmash |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2508.06604v2 (pdf) |
| Date submitted: | Sept. 8, 2025, 1:58 p.m. |
| Submitted by: | Daniel Bulmash |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
Conceptual clarifications of LHS spectral sequence as used in Sec. IV.G. Cross-checks of cohomology group computations for matching results with the crystalline equivalence principle.
Abstract
Modulated symmetries are internal symmetries which do not commute with spatial symmetries; dipolar symmetries are a prime example. We give a general recipe for constructing topological phases protected by modulated symmetries via a defect network construction, generalizing the crystalline equivalence principle to modulated symmetries. We demonstrate that modulated symmetries can be treated identically to unmodulated symmetries in the absence of spatial symmetries, but in the presence of spatial symmetries, some defect networks which are non-anomalous for unmodulated symmetries become anomalous for modulated symmetries. We apply this understanding to classify symmetry-protected topological phases protected by translation symmetry plus either discrete or continuous dipolar symmetries in (1+1)D and (2+1)D and obtain a number of other (1+1)D classification results for modulated symmetry-protected topological phases.
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
Strengths
- Establishes broad definition of modulated symmetry
- Establishes a broad framework for defining modulated SPT in the language of defect network construction
Weaknesses
- Highly mathematical nature of the exposition makes the reading somewhat challenging
Report
Requested changes
none
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)