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Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks

by Juraj Hasik, Didier Poilblanc, Federico Becca

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Juraj Hasik · Didier Poilblanc
Submission information
Preprint Link: scipost_202011_00009v2  (pdf)
Code repository:
Date accepted: 2021-01-13
Date submitted: 2020-12-31 17:51
Submitted by: Hasik, Juraj
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


The recent progress in the optimization of two-dimensional tensor networks [H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X 9, 031041 (2019)] based on automatic differentiation opened the way towards precise and fast optimization of such states and, in particular, infinite projected entangled-pair states (iPEPS) that constitute a generic-purpose Ansatz for lattice problems governed by local Hamiltonians. In this work, we perform an extensive study of a paradigmatic model of frustrated magnetism, the J 1 − J 2 Heisenberg an- tiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we re- port accurate estimations of the magnetization curve in the Néel phase for J 2 /J 1 ≤ 0.45. The unrestricted iPEPS simulations reveal an U (1) symmetric structure, which we identify and impose on tensors, resulting in a clean and consistent picture of antiferromagnetic order vanishing at the phase transition with a quantum paramagnet at J 2 /J 1 ≈ 0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

List of changes

Additional references to works on J1-J2 model have been added to Introduction: Series expansions PRB 60, 7278 (1999), PRB 73, 184420 (2006); coupled cluster approach, PRB 78, 214415 (2008), Eur.Phys.J.B 88, 2 (2015); cluster mean-field theory, J. Phys Condens. Mat. 26, 115601 (2014).

The introduction of U(1) symmetry has been changed slightly. Formulas 6,7, and 8 now correctly include dependence
on the group element g \in U(1).

The data from DMRG of Ref 14 and coupled-cluster study of Eur.Phys.J.B 88, 2 (2015) have been added to Fig. 6 for comparison.
Also an inset zooming in on the region 0.39<J2<0.49 has been added.

A short discussion regarding the extension of the presented methodology beyond J2>0.5 has been added to Conclusions.

Data in all but Figure 6 is now presented without error bars. The figures have been repositioned to appear closer
to the point of their first mention in the main text.

Minor grammatical corrections of the text have been added.

Published as SciPost Phys. 10, 012 (2021)

Reports on this Submission

Anonymous Report 3 on 2021-1-5 (Invited Report)


The authors have addressed some of my suggestions of the last review. As the remaining ones are only of cosmetic nature, I recommend the work to be accepted for publication in SciPost Physics.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 2 on 2021-1-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202011_00009v2, delivered 2021-01-05, doi: 10.21468/SciPost.Report.2364


Correlation length is used for the estimations toward large-D limit. This improves the convergence in spontaneous magnetization.


Size of the unit cell limits the parameter range. The case J2 > J1 cannot be treated.


Several rearrangements of figures and a table makes it easy to read through the article. Fine corrections based on comments from other referees are properly done. Again, I recommend the publication of this article.

  • validity: high
  • significance: good
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: perfect

Anonymous Report 1 on 2021-1-2 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202011_00009v2, delivered 2021-01-02, doi: 10.21468/SciPost.Report.2351


The authors have carefully addressed my concerns raised in the last
review and modified the manuscript accordingly.
I would recommend the work to be accepted for publication in SciPost Physics.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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