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

Within the tensor network framework, the (positive) thermal density operator can be approximated by a double layer of infinite Projected Entangled Pair Operators (iPEPO) coupled via ancilla degrees of freedom. To investigate the thermal properties of the spin1/2 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 greater than or similar to 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 ->infinity 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.

Automated summary

The (positive) thermal density operator in the tensor network framework can be approximated by a double layer of infinite iPEPO coupled via ancilla degrees of freedom. A variational optimization is performed on plaquettes to investigate the thermal properties of the spin1/2 Heisenberg model, showing accurate behavior of various observables and validating the imaginary-time evolution procedure. The method is extended to frustrated models, with preliminary results shown.