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Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice

by Francesco Ferrari, Sen Niu, Juraj Hasik, Yasir Iqbal, Didier Poilblanc, Federico Becca

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Submission summary

Authors (as registered SciPost users): Francesco Ferrari · Juraj Hasik · Yasir Iqbal · Didier Poilblanc
Submission information
Preprint Link: scipost_202212_00062v2  (pdf)
Date accepted: 2023-04-03
Date submitted: 2023-02-20 13:40
Submitted by: Ferrari, Francesco
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Computational
Approach: Computational


Motivated by recent experiments on Cs2Cu3SnF12 and YCu3(OH)6Cl3 , we consider the S=1/2 Heisenberg model on the kagome lattice with nearest-neighbor super-exchange J and (out-of-plane) Dzyaloshinskii-Moriya interaction JD , which favors (in-plane) Q=(0, 0) magnetic order. By using both variational Monte Carlo and tensor-network approaches, we show that the ground state develops a finite magnetization for JD/J≳0.03-0.04; instead, for smaller values of the Dzyaloshinskii-Moriya interaction, the ground state has no magnetic order and, according to the fermionic wave function, develops a gap in the spinon spectrum, which vanishes for JD → 0. The small value of JD/J for the onset of magnetic order is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu3(OH)6Cl2 . For this reason, we assess the spin dynamical structure factor and the corresponding low-energy spectrum, by using the variational Monte Carlo technique. The existence of a continuum of excitations above the magnon modes is observed within the magnetically ordered phase, with a broad peak above the lowest-energy magnons, similarly to what has been detected by inelastic neutron scattering on Cs2Cu3SnF12.

Author comments upon resubmission

Dear Editor,

we would like to resubmit the revised version of the manuscript which includes changes addressing the requests made by the referees. We have replied to the comments of the referees and highlighted the changes made to the manuscript.

Sincerely yours,
Francesco Ferrari (on behalf of all the authors)

List of changes

-we included the revised estimates of J_D/J for Herbertsmithite (Section 1)
-we updated Fig.4 and 5 to include the results for J_D=0
-we improved the discussion of the results for the magnetization in comparison to previous works based on exact diagonalization (Section 3.1)
-we commented about the possible separate fitting of iPEPS and iPESS data (Section 3.1)
-we improved the discussion about the broad peak observed in our spectra at Gamma' above the magnon modes and the comparison to experimental results (Section 3.2)
-we improved the discussion in the appendices (mostly Appendix A); we updated Fig.11-12, correcting minor typos and improving the clarity of the plots
-we added a paragraph to discuss the comparison of our spectra to previous results at the end of Appendix C
-we corrected minor typos throughout the manuscript
-we added new references

Published as SciPost Phys. 14, 139 (2023)

Reports on this Submission

Report 4 by Philippe Mendels on 2023-3-13 (Invited Report)

  • Cite as: Philippe Mendels, Report on arXiv:scipost_202212_00062v2, delivered 2023-03-13, doi: 10.21468/SciPost.Report.6890


The authors have replied to all comments except two, see below. The first one can be discarded, the second one, I leave it at this stage as optional.

1- My item 4 of the previous report (~add a Zeeman term to the Hamiltonian) has certainly been considered by the authors as an avenue for future work. This sounds fair.

2- I cite one statement from my item 1 of the previous report "In any case, the authors would predict that the QSL state should be gapped, whereas this does not seem to be the case [P. Khuntia et al., Nature Physics 16, 469-474 (2020)], an issue still debated; maybe I missed the point but it would be useful to have that value of the gap (possibly vs J_D/J)".
My comment is: Can the value of the gap be clearly plotted in Appendix B, fig. 13 ?

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Author:  Francesco Ferrari  on 2023-03-14  [id 3476]

(in reply to Report 4 by Philippe Mendels on 2023-03-13)
answer to question

Concerning the second point of the referee, we mention that a numerical evaluation of the gap size in the thermodynamic limit is an extremely demanding task, because it requires several (additional) calculations of the dynamical structure factor on different lattice sizes and for different values of J_D/J. Furthermore, within the spin-liquid region very long numerical simulations are necessary in order to obtain small statistical errors. For this reason, we would like to defer the precise numerical evaluation of the gap to a possible future work.
To further clarify this point, we will include a sentence in the appendix of the revised manuscript to remark that the presence of a gapped spin-liquid phase is inferred from the spectrum of the *unprojected* Hamiltonian, while the precise estimation of the gap can be obtained only by a numerical calculation of the Gutzwiller-projected states, which goes beyond the scope of this work.

Anonymous Report 2 on 2023-3-3 (Invited Report)


The authors have taken the referee remarks into account and provided a revised manuscript that I can now recommend for publication.

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Report 1 by Samuel Bieri on 2023-2-22 (Invited Report)


I think that the authors have responded to all questions of the referees in a convincing way. I therefore suggest the manuscript to be published in this form.

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