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Anyon condensation in mixed-state topological order
by Ken Kikuchi, Kah-Sen Kam, Fu-Hsiang Huang
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Fu-Hsiang Huang |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2406.14320v3 (pdf) |
| Date submitted: | July 24, 2025, 10:57 a.m. |
| Submitted by: | Fu-Hsiang Huang |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We discuss anyon condensation in mixed-state topological order. The phases were recently conjectured to be classified by pre-modular fusion categories. Just like anyon condensation in pure-state topological order, a bootstrap analysis shows condensable anyons are given by connected \'etale algebras. We explain how to perform generic anyon condensation including non-invertible anyons and successive condensations. Interestingly, some condensations lead to pure-state topological orders. We clarify when this happens. We also compute topological invariants of equivalence classes.
List of changes
- For the first comment, we put the superscript
phon the first theorem to emphasize this is not a mathematical theorem but a physical result and for the other three theorems we cited math papers. - For the second comment, we shortened the paper by cutting one appendix.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2025-7-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2406.14320v3, delivered 2025-07-29, doi: 10.21468/SciPost.Report.11657
Strengths
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The paper addresses an interesting question (what happens when anyons condense in mixed states rather than pure states?)
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The paper illustrates the discussion with plenty of examples
Weaknesses
Even after the revision, the presentation is still misleading:
1- The authors now call their first result' aphysical theorem'. There is no such thing. Theorem are statements whose validity is established by a proof . Physical truth' can be established by mathematical proof or by empirical evidence. Neither is provided for thephysical theorem' in this paper. It is a conjecture backed up by a general discussion and some examples, so it should be called a conjecture.
2- The status of the other theorems is also not clearly stated. The authors now cite other papers, suggesting that the theorems were fully formulated and proved in those papers. However, they introduce the theorems by saying `We clarified'. What exactly is the clarification here? Is it the application to physics, and the illustration with examples? That would be acceptable, but should be stated clearly.
Report
Requested changes
1- The `physical theorem' should be called Conjecture
2- In the introductory paragraphs of the other three theorems the authors should state clearly what they are contributing in this paper: `We discuss and illustrate the following theorem' or similar.
Recommendation
Ask for minor revision