SciPost Submission Page
On the relation between fractional charge and statistics
by Thors Hans Hansson, Rodrigo Arouca, Thomas Klein Kvorning
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Rodrigo Arouca · Hans Hansson · Thomas Klein Kvorning |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2412.15857v1 (pdf) |
| Date submitted: | Jan. 8, 2025, 9:53 a.m. |
| Submitted by: | Arouca, Rodrigo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We revisit an argument, originally given by Kivelson and Ro\v{c}ek, for why the existence of fractional charge necessarily implies fractional statistics. In doing so, we resolve a contradiction in the original argument, and in the case of a ν=1/m Laughlin holes, we also show that the standard relation between fractional charge and statistics is necessary by an argument based on a t'Hooft anomaly in a one-form global Zm symmetry.
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
1- closes the loophole in the original argument on the relation between fractional charge and fractional statistics in FQHE and similar phases of matter.
2- establishes relation between the problem and t'Hooft anomalies for 1-form symmetries
3- clearly written
4- gives necessary references
Weaknesses
1- Possible generalizations of the presented argument are not discussed (see the report)
Report
The manuscript revisits old arguments relating fractional charge and statistics in gapped systems such as FQHE. The authors show how the loophole in the classical argument can be closed. The key ideas are:
- assume that the system does not support neutral excitations with fractional statistics.
- Show that there is an obstruction in removing integer fluxes from composite objects with several fluxes.
- The latter is shown by showing the inconsistency of the obtained theory (after removal) due to t'Hooft anomaly for the global Z_m symmetry present in the Chern-Simons action for fractional charge of elementary excitations.
I find the arguments convincing and worth publishing in SciPost Physics. There are few open questions that are only partially addressed/mentioned in the manuscript.
- The internal structure of composite objects and fractional spin. It seems plausible that coupling additionally the system with gravitational background one could generalize the argument proving the fractional charge of the fractional excitations. It probably can be done using constructions discussed in
X. Wen and A. Zee, Phys. Rev. Lett., 69, 953 (1992).
and the ideas of framing and framing anomalies
G. Y. Cho, etal. Phys. Rev. B, 90, 115139 (2014),
A. Gromov etal, Phys. Rev. Lett. 114, 016805 (2015).
- Let us assume that there are multiple species of fractionally charged particles and particles with fractional statistics (including possibly neutral particles). It seems that the t'Hooft anomalies discussed in the manuscript would provide some constraints on possible content in terms of charges, spins and statistics of excitations. It might be interesting to see these more general relations.
While manuscript would benefit, I think, from discussions of these generalizations, it might be a subject of a separate work.
Requested changes
1- The paragraph starting with "Concerning the internal structure of the quasiparticles..." on page 5 is repeated twice. Please, remove one of those.
2- Few comments related to the generalizations mentioned in the report section would be appreciated but are Optional.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
This is an excellent paper. The authors revisit an old argument which argued that fractional charge implies fractional statistics and showed that had a serious loophole. They they furnished a complete proof by using both heuristic arguments and modern methods of generalized symmetries and quantum anomalies . The paper is well written and conceptually self-contained. It clarifies the physical linkage between these concepts . It is clearly a very valuable new addition to the literature on this subject.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Author: Rodrigo Arouca on 2025-04-01 [id 5325]
(in reply to Report 1 on 2025-02-17)Thank you for your kind and thorough review. We truly appreciate your positive feedback.
Author: Rodrigo Arouca on 2025-04-01 [id 5326]
(in reply to Report 2 on 2025-02-21)We thank you for your thorough reading of our manuscript and are pleased you find it suitable for publication in SciPost. We also appreciate you identifying the typo (which is now corrected) and your insightful suggestion to consider relations between fractional spin, statistics, and charge, rather than only the latter two. While this direction is indeed intriguing, we believe a more detailed discussion would deviate from our main message and is better suited for a separate publication.