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Itinerant ferromagnetism in dilute SU(N) Fermi gases
by Jordi Pera, Joaquim Casulleras, Jordi Boronat
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Submission summary
| Authors (as registered SciPost users): | Jordi Boronat |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2205.13837v3 (pdf) |
| Date submitted: | 2022-10-27 10:44 |
| Submitted by: | Boronat, Jordi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of an old result that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.
Author comments upon resubmission
Here we resubmit our manuscript with the changes suggested by the Referees.
J. Pera, J. Casulleras, J. Boronat
List of changes
This is reported in our replies to the Referees.
Current status:
Reports on this Submission
Report
In the revised version the authors address the issues raised in the first round of review satisfactorily, and I now recommend publication in SciPost Phys.
Requested changes
Clarification:
- based on the author response to Concern #1 of report II it seems the data in Fig. 9 is rescaled by 0.2(2π)^2, but the manuscript still states "(2π)^2", e.g. in the caption of Fig.9 and in the paragraph just above the figure.
This should be clarified for the final version.
Report #2 by Anonymous (Referee 2) on 2022-10-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2205.13837v3, delivered 2022-10-28, doi: 10.21468/SciPost.Report.6005
Strengths
1- The manuscript is very thorough and presents detailed calculations of the derived analytic expressions for the energy of repulsive Fermi gases up to 2nd order of perturbation theory in the gas parameter.
2- Provides clear insight into the nature of the ferromagnetic transition for $s\geq 1/2$.
Report
Authors have satisfactorily answered the questions in my report and incorporated the requested changes. In particular, the more detailed comparison against experiments and prior theoretical approaches, as well as the discussion with respect to previous theoretical results studying SU(N) imbalanced mixtures has strengthened the manuscript.
I recommend publication in SciPost Phys after the following minor comment is addressed:
1. In Fig 10, why does the s=1/2 red cross do not match with the green line? I expect they should.
Requested changes
1- Explain/correct the discrepancy in Fig. 10.
Author: Jordi Boronat on 2022-11-03 [id 2978]
(in reply to Report 2 on 2022-10-28)
We kindly thank the Referee for his/her positive comments and for finding our manuscript appropriate for SciPost Phys. In the following, we address the comment pointed out by the Referee and the changes introduced in the manuscript accordingly.
Concern 1
In Fig 10, why does the $s=1/2$ red cross do not match with the green line? I expect they should. Explain/correct the discrepancy in Fig. 10.
Author: The green and yellow lines in Fig. 10 are only valid when, at the transition, the polarization goes directly from 0 to 1; this is the case for $s>1/2$. However, at $s=1/2$ the Stoner model predicts a continuous transition, and the second-order approximation predicts a transition to a polarization of 0.545, hence the green and yellow lines do not apply at $s=1/2$. That is the origin of the discrepancy. This exception was already commented in the previous version ,below Eq. (30). However, and to be even more clear on this point, we have written the following additional sentence.
" Notice that for $s=1/2$ Eqs. (29) and (30) do not hold. "
Author: Jordi Boronat on 2022-11-03 [id 2977]
(in reply to Report 1 on 2022-10-28)We kindly thank the Referee for for finding our manuscript appropriate for SciPost Phys. In the following, we address the comment pointed out by the Referee.
Concern 1:
Clarification: - based on the author response to Concern 1 of report II it seems the data in Fig. 9 is rescaled by $0.2(2\pi)^2$, but the manuscript still states "$(2\pi)^2$", e.g. in the caption of Fig. 9 and in the paragraph just above the figure. This should be clarified for the final version.
Author: We are sorry because we made a type editing mistake when we wrote the answers to the Referee report. The correct value that we use to scale the experimental points is $(2\pi)^2$, which is the value reported in the manuscript.