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We use non-perturbative linked-cluster expansions to determine theground-state energy per site of the spin-one Heisenberg model on the kagomelattice. To this end, a parameter is introduced allowing to interpolate betweena fully trimerized state and the isotropic model. The ground-state energy persite of the full graph decomposition up to graphs of six triangles (18 spins)displays a complex behaviour as a function of this parameter close to theisotropic model which we attribute to divergencies of partial series in thegraph expansion of quasi-1d unfrustrated chain graphs. More concretely, thesedivergencies can be traced back to a quantum critical point of theone-dimensional unfrustrated chain of coupled triangles. Interestingly, thereorganization of the non-perturbative linked-cluster expansion in terms ofclusters with enhanced symmetry yields a ground-state energy per site of theisotropic two-dimensional model being in quantitative agreement with othernumerical approaches in favor of a spontaneous trimerization of the system. Ourfindings are of general importance for any non-perturbative linked-clusterexpansion on geometrically frustrated systems.

Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model