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Localized dopant motion across the 2D Ising phase transition
by K. Knakkergaard Nielsen
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Submission summary
| Authors (as registered SciPost users): | Kristian Knakkergaard Nielsen |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2404.11608v2 (pdf) |
| Date submitted: | 2024-06-17 09:37 |
| Submitted by: | Knakkergaard Nielsen, Kristian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational, Phenomenological |
Abstract
I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings $J$, the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude $t$. The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [arXiv:2310.11193] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, $k_BT / |J|$, and on the ratio of the spin coupling to the hopping $J/t$. I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.
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
Author comments upon resubmission
List of changes
1) More extensively cite early papers dealing with the motion of dopants in quantum magnets (Introduction).
2) An extensive discussion (Sec. 5) of the results and how the investigated mixed-dimensional model may be generalised and the robustness of the discovered effects tested. This includes discussing: beyond 1D dopant motion, beyond the Ising model, increasing the doping level, connecting to an external bath.
3) Figure 3 and the associated text has been modified to more carefully explain the localisation mechanism at high temperatures.
4) Minor typos in equations (10) and (15) have been corrected.
Current status:
Reports on this Submission
Report
I share the opinion of the 1st referee: the setup of a hole moving along a line does not seem physical and does not give real insights into the true 2d physical problem. As a simple extension of previous work on ladder geometry, this work is more appropriate to the SciPost Physics Core.
Recommendation
Accept in alternative Journal (see Report)
Report #1 by Anonymous (Referee 2) on 2024-6-26 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2404.11608v2, delivered 2024-06-26, doi: 10.21468/SciPost.Report.9303
Report
I appreciate the reply of the author, in particular, the extended discussion section that was added to the resubmitted manuscript. However, in light of this discussion, I can not recommend the publication of the paper in SciPost Physics. My main takeaway is that the physics explored in this work is too special to the somewhat artificial 1d geometry to offer much insight into the behavior of 2d systems. The extended discussion in Sec. 5 essentially just summarizes expectations that rely on what was already known about the localization of electrons in 1d and 2d lattices. I also do not see a clear way to extend the approach applied in this work beyond the special case of 1d hole motion. Moreover, the results presented here, while certainly valuable, essentially confirm the naive picture of localization in 1d for arbitrarily weak disorder (in the ferromagnetic case), or the presence of a linear confining potential (in the antiferromagnetic phase). For these reasons, I believe that the paper is better suited for publication in SciPost Physics Core.
Minor comments:
- I appreciate the updated references, with more early works cited. Perhaps the author could expand this list even further (e.g. with Sachdev PRB 39, 12232, or Manousakis RevModPhys 63, 1).
- I think that the fact that localization is actually the expected behavior in the 1d motion of a single particle for arbitrarily weak disorder (~domain wall density), on general grounds, should be explicitly mentioned in the introduction. The current phrasing is implying the opposite.
- I believe that the discussion of the non-monotonous temperature dependence of the localization length around eq. (21) could still be made clearer. If I understand it correctly, l_ave was shown to diverge at infinite temperature. As it decreases with decreasing T, eventually it becomes smaller than l_fl (because of the different scaling with respect to t/J), at which point it becomes the relevant scale of localization. If this intersection happens where l_ave still had a positive slope with respect to T, this tendency has to turn at some T, because the hole becomes delocalized for T=0, so the localization length has to diverge in that limit. Is this correct?
Recommendation
Accept in alternative Journal (see Report)
Author: Kristian Knakkergaard Nielsen on 2024-07-02 [id 4596]
(in reply to Report 1 on 2024-06-26)Response to Reports 1 and 2
I appreciate the comments and objections from the Referees. I, however, do not agree that the current analysis does not inform us about the two-dimensional case, as the Referees imply. Indeed, if one immediately jumped to the 2D scenario and postulated an inverted metal-insulator transition, this would be hard to believe. But because of the detailed analysis in the current Article and the direct, solid evidence of an inverted crossover between these two phases for 1D motion, it is now very plausible that said transition should indeed occur when the hole can move in 2D.
Now please note again, that this is inverted from the usual metal-insulator case, where it is insulating at low temperatures and metallic at high temperatures. The mere existence of an inverted transition is highly nontrivial.
Along the same lines, I remain convinced that without such an analysis as the one performed here, one would not guess that the hole should localize at high temperatures even for 1D motion. It is only as a result of my current, thourough analysis that this becomes clear.
I, however, acknowledge that both Referees recommend publication in SciPost Physics Core, and I accept their recommendation.
Sincerely,
Kristian Knakkergaard Nielsen
Reply to minor comments from Report 1.
1) I thank the Referee for the references. I have included the one from Sachdev in the revised manuscript.
2) I agree with the Referee that the introduction should be slightly more carefully phrased. I have not included the sentence:
"While the hole in a ferromagnetic ground state will certainly delocalize, the same may not remain true as soon as one heats up the system by any infinitesimal amount. Indeed, when the system is not at zero temperature, occasional spin flips may act as local defects that generically has a localising effect in one dimension due Anderson localisation..."
I do not agree with the Referee, however, that one should expect localization in the current setup \emph{a priori}. Indeed, it is a core result of the paper that the spin flips do in fact work as local impurities for the hole motion.
3) I have made a final revision of the explanation of the non-monotonic behavior of the localization length. Please see the revised text for a full explanation.