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Anyon condensation in mixed-state topological order
by Ken KIKUCHI, Kah-Sen KAM and Fu-Hsiang Huang
Submission summary
| Authors (as registered SciPost users): | Fu-Hsiang Huang |
| Submission information | |
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| Preprint Link: | scipost_202502_00050v1 (pdf) |
| Date submitted: | Feb. 23, 2025, 11:06 a.m. |
| Submitted by: | Huang, Fu-Hsiang |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| 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.
Current status:
Awaiting resubmission
Reports on this Submission
Strengths
- The paper addresses and interesting question (what happens when anyons condense in mixed states rather than pure states?)
- The paper illustrates the discussion with plenty of examples
Weaknesses
- The paper states four main results, calls them
theorems' - but does not contain a formal proof, reference to proof or other argument to justify thetheorems' - The paper is too long
Report
The paper discusses the interesting question of how the discussion of topological order as resulting from the breaking of higher order symmetry is changed when the symmetry breaking state is mixed rather than pure. The introduction states four main results, but these results are only illustrated in the paper, not proven (despite being called theorems). For publication in any journal of theoretical or mathematical physics I would expect clear proofs of theorems, or references to proofs. I would ask the authors to provide the proofs. It is possible that this will extend the length of the paper beyond the page limit in SciPost, in which case an alternative journal may be more suitable.
Requested changes
- Provide proofs of the four theorems
- Shorten the paper
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Ask for major revision