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Anyons in a tight wave-guide and the Tonks-Girardeau gas
by Nicolas Rougerie, Qiyun Yang
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|Authors (as registered SciPost users):||Nicolas Rougerie|
|Preprint Link:||scipost_202303_00024v1 (pdf)|
|Date submitted:||2023-03-21 11:22|
|Submitted by:||Rougerie, Nicolas|
|Submitted to:||SciPost Physics|
We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter $\alpha \in ]0,2[$. In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity $2\pi \alpha$, generating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of $\alpha$.
Submission & Refereeing History
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:scipost_202303_00024v1, delivered 2023-06-17, doi: 10.21468/SciPost.Report.7367
This manuscript explores the physics of 1D systems having fractional statistics which interpolates between usual bosonic and fermionic ones on varying of a statistical parameter α. As the authors pointed out in the introduction, there have been several proposals to obtain anyonic models in one dimension. Several studies focused on e.g. 1D bosonic systems subject to a density-dependent hopping in a way that the resulting 1D model is effectively described by anyonic statistics. On the other hand, in two spatial dimensions, anyonic statistics can naturally emerge from the braiding of two particles, or equivalently, from the Aharonov-Bohm phase picked by the wavefunction in the presence of magnetic flux tubes.
In this context, the authors wish to clarify whether the proposals for 1D anyonic systems can be thought of as a dimensional reduction of 2D anyonic models. In particular, they consider a 2D anyonic model and impose a dimensional reduction by means of a strongly anisotropic trapping potential to obtain an effective 1D model. Their main result is that, independently of α, the resulting 1D model is described by strongly repulsive bosons (Tonks-Girardeau gas).
I have found the paper well-written and scientifically sound, although I haven’t gone into the details of the authors’ proof. I believe that this article deserves publication in some form but I have some perplexities regarding its publications in SciPost Physics. In my opinion, this manuscript would better fit a more specialized journal on mathematical physics.
Indeed, I think that the majority of recent (and less recent) studies on 1D anyons are focused on the consequences of having fractional statistics in one dimension (whose physics quite differs from 2D) rather than relating 1D to 2D anyonic models. Moreover, several studies proposed techniques to experimentally engineer 1D anyons (e.g. Cardarelli et al., Phys. Rev. A 94, 023615 (2016); Keilmann et al., Nat. Commun. 2, 361 (2011) ).
To conclude, I believe that the manuscript would benefit if the authors decide to include more mathematical details on the proof for a more specialized audience. In its current form, I think that the manuscript does not meet the acceptance criteria required for publishing in SciPost Physics.
- Cite as: Anonymous, Report on arXiv:scipost_202303_00024v1, delivered 2023-06-06, doi: 10.21468/SciPost.Report.7317
The authors consider the problem of dimensional reduction for a model of 2D non-interacting anyons. Namely, starting from a 2D system, they consider adding a strong confining potential along one dimension to constrain the motion along the other. Their main result is a mathematical theorem. It states that, in the limit of very strong confining potential, the dynamics is mapped onto a collection of one dimensional systems described by the Tonks-Girardeau Hamiltonian. In particular, there is no dependence on the original exchange statistics parameter, so that the one-dimensional systems are always trivially fermionic.
I believe the draft is well written and clear. However, I am a bit hesitant to recommend publication for the reasons below:
1) First, the main physical message was already found, or at least strongly suggested by, other works in the literature almost 30 years ago, as also mentioned by the authors (see Ref. , ). Therefore, the main contribution of the work is mainly technical, consisting of the mathematical proof of the theorem.
2) On the other hand, in this letter-looking draft, all the mathematical details are omitted. I believe this choice would be justified in the case the result by itself is new, or when the details of the calculations hide the main physical discussions. Here, however, it seems to me the mathematical theorem is the main result. Therefore, given the scope of Scipost, I would find it hard to recommend publication of the draft as is, without substantiating the technical contributions. This could be done by adding one or more appendices.
3) Finally, in my opinion the topic is not so timely. The authors have described one experimental protocol to reduce a 2D anyonic system into 1D ones. As I said, similar conclusions were put forward already in the 90's (see Ref. ). However, in the past decades different experimental proposals have been put forward to realize genuine anyonic statistic in one-dimensional cold-atomic systems (see for instance the very recent paper https://arxiv.org/abs/2306.01737). I think it would be useful if the authors could discuss a bit more how this work relates to these recent developments.
In any case, I don't think the paper is suitable for Scipost Physics, and I believe Scipost Physics Core would be a more appropriate choice for this submission.