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Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
by Shenghan Jiang, Panjin Kim, Jung Hoon Han, Ying Ran
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Shenghan Jiang |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/1610.02024v2 (pdf) |
| Date submitted: | April 24, 2019, 2 a.m. |
| Submitted by: | Shenghan Jiang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The properties of ground state of spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and $Z_2$ topological order leads to different types of $Z_2$ spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a $U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2019-5-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1610.02024v2, delivered 2019-05-24, doi: 10.21468/SciPost.Report.970
Strengths
1- New numerical methods brought to bear on an old problem 2- Compelling evidence for the U(1) spin liquid being at least very nearly degenerate with the true ground state
Weaknesses
1- Relies on empirical extrapolation of energy in the truncation used to compute energies, which may be unreliable.
Report
Overall, I find the paper well-written and relevant. The numerics seem to be carried out carefully; while some of the methods are rather new and their performance poorly understood, the authors point out quite explicitly that this is the case (for example that the energy extrapolation used in Fig. 4 is purely empirical).
Indeed, this extrapolation seems crucial to the paper. It is quite notable that for a given D_cut, the two states are not even close to degenerate, and only after extrapolation, they become degenerate. I would ask that the authors include exactly what fit parameters were used, which will help assessment and later reproducibility of the results. Also, judging from the plot, the exponents for the two lowest states must be quite different - do the authors have an explanation of why that would be the case? Ideally, the authors could also perform some sort of robustness analysis of their fit.
With the small modifications suggested above, the paper can be published.
Requested changes
1- List fit coefficients. 2- Ideally perform robustness analysis of the fit.
Report #1 by Didier Poilblanc (Referee 1) on 2019-5-17 (Invited Report)
- Cite as: Didier Poilblanc, Report on arXiv:1610.02024v2, delivered 2019-05-17, doi: 10.21468/SciPost.Report.958
Strengths
Weaknesses
Report
i) it was initially submitted on arXiv at the same time (even a week before) as the above mentioned PRL, while drawing similar strong conclusions.
ii) it follows a different route, using state-of-the-art tensor symmetry analysis, enabling to construct fully SU(2)-symmetric ansatz while in the non-symmetric TN version a spurious finite 120-degrees magnetic order at all finite D (the tensor bond dimension) values appears.