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

### Submission summary

 As Contributors: Fabien Alet · Didier Poilblanc Arxiv Link: https://arxiv.org/abs/2010.07828v2 (pdf) Date accepted: 2021-01-13 Date submitted: 2020-12-24 13:56 Submitted by: Poilblanc, Didier Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Condensed Matter Physics - Computational Approach: Theoretical

### Abstract

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.

Published as SciPost Phys. 10, 019 (2021)

### List of changes

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

### Submission & Refereeing History

Resubmission 2010.07828v2 on 24 December 2020
Submission 2010.07828v1 on 26 October 2020

## Reports on this Submission

### 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

Accept the revised manuscript

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

### Strengths

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.

### Weaknesses

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

### Report

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