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Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality
by Fabrizio Oliviero, João Augusto Sobral, Eric C. Andrade, Rodrigo G. Pereira
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Submission summary
| Authors (as registered SciPost users): | Eric Andrade · Fabrizio Oliviero |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2112.03327v3 (pdf) |
| Data repository: | https://github.com/joaosds/suppl_noncoplanar |
| Date submitted: | 2022-06-15 14:20 |
| Submitted by: | Oliviero, Fabrizio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Chiral three-spin interactions can suppress long-range magnetic order and stabilize quantum spin liquid states in frustrated lattices. We study a spin-1/2 model on the kagome lattice involving a staggered three-spin interaction $J_\chi$ in addition to Heisenberg exchange couplings $J_1$ on nearest-neighbor bonds and $J_d$ across the diagonals of the hexagons. We explore the phase diagram using a combination of a classical approach, parton mean-field theory, and variational Monte Carlo methods. We obtain a variety of noncoplanar magnetic orders, including a phase that interpolates between cuboc-1 and cuboc-2 states. In the regime of dominant $J_{\chi}$, we find a classically disordered region and argue that it may harbor a gapless chiral spin liquid with a spinon Fermi surface. Our results show that the competition between the staggered three-spin interaction and Heisenberg exchange interactions gives rise to unusual ground states of spin systems.
Author comments upon resubmission
Thank you for the opportunity to submit our paper once more for the SciPost physics journal. We believe the additional changes have helped us to substantially improve our manuscript. We thank both referees for the constructive comments on our manuscript and the opportunity to answer their questions. Our responses were posted on the submission webpage and are viewable online.
Sincerely,
The Authors.
List of changes
List of changes suggested by the first referee:
• Added a few sentences in the introduction to emphasize the novelty of our results.
• Added comment about relation to standard octahedral state.
• Added information about system sizes used in section 3.
• Changed color of arrows in Fig. 3 and added names of the phases.
• Added information that Jd>0 to the caption of Fig. 4.
• Expanded the first paragraph of section 4 to clarify choice of mean-field Ansatz.
• Changed “SU(2)” to “U(1)” gauge redundancy below Eq. 5.
• Corrected plot labels in Fig. 6.
• Added discussion about fixed parameters and boundary conditions used in the VMC in section 5.
• Added appendix about the derivation of Eq. 7.
• Corrected a few typos, including capital letters in the bibliography.
List of changes suggested by the second referee
• Added a new sentence after eq. (18) about the definition of the magnetization.
• Added new sentences to the caption of Fig. 3 about the intensity of Bragg peaks and definition of the 1st and extended Brillouin zone.
• Added a new reference to Phys. Rev. B 91, 041124 (2015) to the 2nd paragraph of the introduction as recommended by the referee.
Current status:
Reports on this Submission
Report
The authors replied to my questions except for the first one, when I wrote "Most importantly...". I insist that, at the classical level, such a disordered state is quite strange and possibly is the result of (a possibly large) degeneracy. May the authors try to see if this is true, by performing additional simulations?
Requested changes
see above
Author: Fabrizio Oliviero on 2022-07-01 [id 2625]
(in reply to Report 1 on 2022-06-21)We sincerely apologize to the referee. In editing our reply, we left our response to this point. This was our mistake and by no means it meant we judged the question posed was unimportant. In the last paragraph of page 6, we briefly argue that the classical ground state shows at least a U(1) degeneracy close to J1=Jd=0, similar to the usual antiferromagnetic Heisenberg model in the kagome lattice, and unraveling the link between classical disorder and degeneracy. To further explore this general argument, we add an Appendix (see file "appendixA.pdf" attached) to the new version where we focus on a subset of classically degenerate ground states, the so-called triaxial states, following the discussion of Ref. 42. The triaxial states show an extensive degeneracy, 2^(N/6), and a perturbative investigation of their stability allows us to qualitatively understand the shape of the disordered region in the phase diagram.
Attachment:
appedixA.pdf
Anonymous on 2022-07-06 [id 2642]
(in reply to Fabrizio Oliviero on 2022-07-01 [id 2625])I thank the authors for this explanation. The paper is now suitable for publication.