SciPost Submission Page
Localized dopant motion across the 2D Ising phase transition
by K. Knakkergaard Nielsen
Submission summary
| Authors (as registered SciPost users): | Kristian Knakkergaard Nielsen |
| Submission information | |
|---|---|
| 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
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)