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Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice

by Didier Poilblanc, Matthieu Mambrini, Fabien Alet

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Submission summary

Authors (as registered SciPost users): Fabien Alet · Matthieu Mambrini · Didier Poilblanc
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-01-13
Date submitted: 2020-12-24 13:56
Submitted by: Poilblanc, Didier
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approach: Theoretical


Within the tensor network framework, the (positive) thermal density operator can be approximated by a double layer of infinite Projected Entangled Pair Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the thermal properties of the spin-1/2 Heisenberg model on the square lattice, we introduce a family of fully spin-$SU(2)$ and lattice-$C_{4v}$ symmetric on-site tensors (of bond dimensions $D=4$ or $D=7$) and a plaquette-based Trotter-Suzuki decomposition of the imaginary-time evolution operator. A variational optimization is performed on the plaquettes, using a full (for $D=4$) or simple (for $D=7$) environment obtained from the single-site Corner Transfer Matrix Renormalization Group fixed point. The method is benchmarked by a comparison to quantum Monte Carlo in the thermodynamic limit. Although the iPEPO spin correlation length starts to deviate from the exact exponential growth for inverse-temperature $\beta \gtrsim 2$, the behavior of various observables turns out to be quite accurate once plotted w.r.t the inverse correlation length. We also find that a direct $T=0$ variational energy optimization provides results in full agreement with the $\beta\rightarrow\infty$ limit of finite-temperature data, hence validating the imaginary-time evolution procedure. Extension of the method to frustrated models is described and preliminary results are shown.

List of changes

All changes have been described in the detailed answers to the 3 referee reports.

Published as SciPost Phys. 10, 019 (2021)

Reports on this Submission

Anonymous Report 3 on 2021-1-10 (Invited Report)


The authors have addressed all the points in the revised version and I can thus recommend publication of this paper.

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

Report 2 by Jürgen Schnack on 2021-1-6 (Invited Report)


Accept the revised manuscript

  • validity: -
  • significance: -
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Anonymous Report 1 on 2021-1-5 (Invited Report)


Symmetry in the target physical system is considered from the structure of local tensors. This construction greatly reduce the number of parameters considered in numerical optimization.


Since the approach fits to systems with high symmetry, generalization to systems with lower symmetry or random systems is not straight forward.


The authors have properly revised the manuscript. Now the explanation of Figures 3 and 4 are satisfactory. Thus I recommend the publication of this article.

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

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