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

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