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Tensor network study of the Shastry-Sutherland model with weak interlayer coupling

by Patrick C. G. Vlaar, Philippe Corboz

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Submission summary

Authors (as registered SciPost users): Patrick Vlaar
Submission information
Preprint Link:  (pdf)
Date submitted: 2023-02-22 16:42
Submitted by: Vlaar, Patrick
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


The layered material SrCu$_2$(BO$_3$)$_2$ has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu$_2$(BO$_3$)$_2$ under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around $J''/J\sim0.04-0.05$ than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu$_2$(BO$_3$)$_2$ to be around $J''/J\sim0.026$ at ambient pressure.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2023-5-4 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2302.07894v1, delivered 2023-05-04, doi: 10.21468/SciPost.Report.7140


1- One of the first state-of-the-art calculation for a 3d frustrated quantum magnet
2- This paper provides an estimate of the weak interplane coupling for one of the most studied quantum material


1- In order to compute the phase diagram, the authors compare energies of various phases. This is done using 1/D extrapolations (where D is the control parameter, i.e. the tensor bond dimension). However these extrapolations do not appear very reliable (the scaling is far from linear).
2- More importantly, the nature of the intermediate phase (full plaquette vs empty plaquette) seems to disagree with current experiments, so that the microscopic model is probably not valid ?


This paper provides one of first tensor-network application to 3d frustrated quantum magnets. The team has a well-known expertise on this material and has already contributed to several studies of the 2d model. Recently, they have proposed an elegant algorithm to tackle a weak 3d coupling, which has been benchmarked on simpler models (where stochastic quantum Monte-Carlo simulations are possible). Hence, it is very interesting to see a more realistic simulation of this 3d model, especially given that other methods have tried in the past to estimate the 3d coupling (for instance series expansion).

Although the 3d model might not be fully realistic for the material (see weakness 2), it is interesting in its own. This paper is nicely written and provides compelling evidence that the 3d coupling is much smaller than previously anticipated.

Requested changes

1- How could the authors explain the discrepancy with susceptibility fits ? Isn't it related to the fact that the microscopic model is not adequate ? I would suggest to add a discussion about the modelling in the introduction.
2- Would it be possible to perform a finite correlation length scaling, especially in the Néel phase, to see if it improves the extrapolated value ?

  • validity: high
  • significance: high
  • originality: good
  • clarity: top
  • formatting: excellent
  • grammar: excellent

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Anonymous on 2023-04-19  [id 3598]

The paper explores ground state properties of the three-dimensional Shastry-Sutherland model. By means of the Tensor network method recently developed, the authors determine the phase diagram correctly. Therefore, this work is, of course, suitable for publication.

Short comment:
The three-dimensional orthogonal dimer model has first been discussed by Ueda & Miyahara.
(Kazuo Ueda and Shin Miyahara 1999 J. Phys.: Condens. Matter 11 L175) Therefore, this paper should be cited.

Author:  Patrick Vlaar  on 2023-04-28  [id 3630]

(in reply to Anonymous Comment on 2023-04-19 [id 3598])
answer to question

Thank you for the positive assessment of our work and for pointing out the reference. We will include it in the revised version.