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Universal Properties of Anisotropic Dipolar Bosons in Two Dimensions
by J. Sánchez-Baena, L. A. Peña Ardila, G. Astrakharchik, F. Mazzanti
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Submission summary
| Authors (as registered SciPost users): | G. E. Astrakharchik · Ferran Mazzanti · Luis Peña Ardila · Juan Sánchez-Baena |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2112.11094v1 (pdf) |
| Date submitted: | 2021-12-26 09:49 |
| Submitted by: | Mazzanti, Ferran |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter $x=n a_0^d$, with $n$ the density, $d$ the dimensionality of the space ($d=1,2,3$) and $a_0$ the $s$-wave scattering length. The universal regime typically extends up to $x\approx 0.001$, while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes $a_0$ depend on the polarization angle $\alpha$, so different combinations of $n$ and $\alpha$ can lead to the same value of the gas parameter $x$. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large values of the gas parameter $x$. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of $x$ that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-3-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2112.11094v1, delivered 2022-03-01, doi: 10.21468/SciPost.Report.4582
Strengths
1) Extensive numerical analysis.
2) Clear presentation of the results.
3)Substantial novelty.
3) High impact topic.
Weaknesses
1) Lacking connection with existing literature.
2) Finite size scaling not reported.
Report
I read the paper with interest and I can certainly praise the neat presentation and the well delineated physical questions. The argument (universality in dipolar quantum gases) is highly relevant to AMO physics and this extensive numerical analysis will certainly attract the interest of many experts in the community.
The choice of presenting the numerical picture without pushing a definite theoretical interpretation helps to keep the article focused and improves its quality rather than reducing it. The observation of an extended universal scaling well beyond the expectations of local gases is certainly relevant and will surely produce several further theoretical investigations in the future.
Nevertheless, before the article is formally accepted the authors shall make a more substantial effort to connect their current picture with previous findings in the literature. Indeed, the small number of references in this paper is not justified, since the topic of universality in Bose gases has been extensively studied in the last decade.
The inadequate framing of the article in the literature is particularly evident in the discussion of universality for local interactions in d=2, where the authors refer to the book of Popov, Ref.[17], where ln|ln(x)| corrections to the mean-field universality of a weakly interacting Bose gas in 2D are discussed.
This picture is known to be incomplete, as the ln|ln(x)| terms are only observed in a negligible window of the interaction strength. The actual corrections are logarithmic ln|\mu x|, where \mu is a large experimental parameter \mu~380 according to numerical simulations
see Refs.
1) https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.270402
2) https://journals.aps.org/pra/abstract/10.1103/PhysRevA.66.043608
In particular, see the discussion below Eq. (3) in Ref. (1), which describes the impossibility to achieve the ln|ln(x)| correction regime. Notice that these studies have produced quite an impact in the community and several theoretical analysis have been devoted to reproduce them. See the RG studies:
3) https://doi.org/10.1103/PhysRevA.85.063607
4) https://doi.org/10.1103/PhysRevB.96.174505.
I encourage the authors to extend their discussion of the results in the light of the existing literature, providing a comparison of their findings with the current picture for local systems rather than with the textbook picture.
Finally, although the numerical analysis appears to be reliable, the paper does not contain any quantitative discussion of the finite size scaling for the system. The only sentence I could find on this aspect is: "We have checked that our results remain essentially unchanged when keeping n constant while increasing N and the box size L."
While I do not want to force the authors to perform an extensive numerical finite size scaling, it will be interesting to have at least a flash on how the convergence of the system to the thermodynamic limit is achieved.
I encourage the authors to extend their work and clarify those points.
Requested changes
1) Increase the discussion of current literature, in particular universality in local Bose gases.
2) Include at least a partial discussion of finite size scaling.
Report #1 by Anonymous (Referee 1) on 2022-2-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2112.11094v1, delivered 2022-02-04, doi: 10.21468/SciPost.Report.4319
Report
Dear Editors,
In the presented manuscript "Universal Properties of Anisotropic Bosons in Two Dimensions", the authors study numerically the effects of dipolar interactions in a purely two-dimensional gas of polarized bosonic dipolar particles as a function of the polarization angle and the gas parameter of the system. More specifically, the energy per particle, the pair distribution function, and the condensation fraction were considered. One of the main results is that, being properly rescaled, the energy per particle demonstrates a universal behavior up to very large values of the gas parameter when there are already strong deviations from the mean-field results.
I find the results of numerical calculation interesting and potentially useful, and I also do not see any reason to question their validity. There are, however, several issues concerning their understanding/interpretation and applicability to real physical systems, which need to be clarified and discussed:
- The authors consider only the dipole-dipole interaction between bosons, completely ignoring any short-range contributions. This situation is, of course, experimentally possible via the Feshbach resonance, but very “singular”. In a typical situation, the short-range part of the interparticle interaction is present. How will the account of a, say, small short range interaction change the results?
- Is the any connection between smallness of the anisotropic terms (at least for the values gas parameter smaller than 100) in the pair distribution function and the universal behavior of the energy per particle?
- As a general comment, I find it strange that the authors do not present any argument which could give a hint to understanding of their numerical findings. Do the authors have some ideas why the found universal behavior of the energy per particles continues to such large values of the gas parameter – practically till the crystallization point around 400? In this respect, I would like to draw the author’s attention to the paper Physical Review Research 3, 013088 (2021) devoted to the exact relations for dipolar quantum gas, which could be potentially helpful.
To conclude, I do not recommend the manuscript in its present form for publication. In my opinion, there are several issues which has to be addressed before the final decision concerning publication can be made.
Yours sincerely,