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

TL;DR

This paper develops a symmetric tensor network method to study finite-temperature properties of the spin-1/2 Heisenberg antiferromagnet on a square lattice, achieving accurate results and validating the approach against quantum Monte Carlo data.

Contribution

The authors introduce a symmetric iPEPO-based tensor network approach with a plaquette Trotter-Suzuki decomposition for finite-temperature analysis of quantum spin models.

Findings

Method accurately reproduces thermodynamic observables.

Correlation length deviations occur at higher inverse temperatures.

Zero-temperature variational energies match infinite-temperature extrapolations.

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.