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Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model
by Alexander Nikolaenko, Ya-Hui Zhang
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Submission summary
| Authors (as registered SciPost users): | Alexander Nikolaenko |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202310_00035v2 (pdf) |
| Date submitted: | 2024-05-21 21:45 |
| Submitted by: | Nikolaenko, Alexander |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling $J_K$ at fixed doping $x$. At large positive $J_K$, we confirm the expected conventional Luttinger liquid phase with $2k_F=\frac{1+x}{2}$ (in units of $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the $J_K \leq 0$ side, our simulation finds the existence of a fractional Luttinger liquid (LL*) phase with $2k_F=\frac{x}{2}$, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL*) phase in higher dimensions. The LL* phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive $J_K$. Then we mainly focus on the `critical regime' between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of $J_K$, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around $0.035 J$) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent $z=+\infty$. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.
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Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2024-6-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202310_00035v2, delivered 2024-06-09, doi: 10.21468/SciPost.Report.9211
Report
With their revised version, the authors have made some improvements, but I was surprised how many important points have not been addressed. For example, I tried to read a revised version, but still had the same font-size issues as in the previous round. Thus, I am afraid that we have not really advanced much since the previous round of review.
In addition, I stumbled across some further minor issues when re-reading the manuscript. See "Requested changes" for further details.
Requested changes
1- The font-size issue with the figures still does need to be addressed. For example, the insets of Fig. 5 look like rescaled full-size figures. However, when rescaling figures, one needs to increase the font size and line widths accordingly. I am afraid that such issues still concern a big fraction of the figures. Maybe some of these would become obsolete during production, but typesetting the manuscript with the SciPost Physics template (see https://scipost.org/SciPostPhys/authoring#manuprep) would help to check.
2- Red text on a dark blue background is a bad idea (see, e.g., Fig. 14), in particular if in addition fonts are tiny.
3- The motivation for this work is still from heavy fermions, but when the authors introduce the model, they change their mind and motivate it from optical lattices. It is fine to appeal to additional motivation, but the transition needs to be made smoother.
4- I believe that the Requested changes in Anonymous Report 2 on 2024-1-2 have been simply ignored.
5- "Transfer matrix technique": maybe it is standard and the method can just be referenced from the literature. However, I do not think that one should introduce new notations in figure captions (specifically here the caption of Fig. 4; note that the term appears again at the bottom left of page 7 and in the caption of Fig. 23).
6- I believe that the label of the horizontal axes of Figs. 4(c,d) should read '$q$' rather that '$x$'.
7- Ref. [11] appears to have been published in Science 377, 1-10 (2022).
8- Ref. [28] was in the meantime published in Phys. Rev. Research 6, 023227 (2024).
9- There are a number of minor typographical issues:
a) Systematic absence of spaces before the \cite command.
b) Missing '$\rangle$' in the definition of $V$ on the third line of the caption of Fig. 3.
c) Strange typesetting of '$J_K$' seven lines below Fig. 3.
d) Missing full stop in '... compressibility $\kappa^{−1}$. In the insulating ...' at the beginning of section III C.
e) Spurious 'to' in 'with to two spin-gapped phases' at the beginning of section IV A.
f) Left column of page 12: Do the authors really mean 'optical' or rather 'optimal' 'doping'?
There are a few further minor typographic and grammatical errors (such as missing articles) that I refrain from listing. However, I believe that the manuscript would benefit from careful proofreading, ideally from a native English speaker.
Recommendation
Ask for major revision
Author: Alexander Nikolaenko on 2024-06-13 [id 4560]
(in reply to Report 1 on 2024-06-09)We thank the referee again, most of their objections are valid and below we present a list of changes we made as requested by the referee.
1) We increased fonts of the insets of Fig. 5.
2) We changed the red color of the Fig. 14 and Fig. 21 to the light green, which is easier to read on blue and increased fonts.
3) We moved the discussion of optical lattices to the Appendix A, now we start directly from the Kondo-lattice model and discuss the obtained phase diagram.
4) We apologize for ignoring the Anonymous Report 2 on 2024-1-2 which we missed. We answered it now. We added the sentence saying that we dropped three-site terms in the end of the appendix. We also stress that ultra-criticality does not require a finite $J_{cs}$ as can be seen in Fig.7,8,9 for example.
5) We moved the discussion of how we obtain the central charge from the captions of Figures 4, 7, 23 to the main text.
6) We have changed labels for Figure 4c),d).
7,8) We updated these references.
9) We corrected these minor typographical mistakes suggested by referee.