Benchmarking global SU(2) symmetry in 2d tensor network algorithms

Abstract

We implement and benchmark tensor network algorithms with SU(2) symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement SU(2)-invariant versions of the infinite Projected Entangled Pair States (iPEPS) and infinite Projected Entangled Simplex States (iPESS) methods. Our implementation of SU(2) symmetry follows the formalism based on fusion trees from [P. Schmoll, S. Singh, M. Rizzi, R. Or\'us, arXiv:1809.08180]. In order to assess the utility of implementing SU(2) symmetry the algorithms are benchmarked for three models with different local spin: the spin-1 bilinear-biquadratic model on the square lattice, and the Kagome Heisenberg antiferromagnets (KHAF) for spin-1/2 and spin-2. We observe that the implementation of SU(2) symmetry provides better energies in general than non-symmetric simulations, with smooth scalings with respect to the number of parameters in the ansatz, and with the actual improvement depending on the specifics of the model. In particular, for the spin-2 KHAF model, our SU(2) simulations are compatible with a quantum spin liquid ground state.