Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet

We investigate the ground-state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site e(0) = -1.41090(2), with D* = 8 multiplets retained (i.e., a bond dimension of D = 24), and e(0) = -1.4116(4) from large-D extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of delta approximate to 19%, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.