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. Orús, 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.

6 pages, 9 figures, 1 table, revised version

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Cited by in corpus (8)

• A beginner's guide to non-abelian iPEPS for correlated fermions
• Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• iPEPS study of spin symmetry in the doped $t$-$J$ model
• Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism
• Variational optimization of projected entangled-pair states on the triangular lattice
• Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry