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arXiv · 1508.05200

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

D. Ixert·T. Tischler·K. P. Schmidt
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Abstract

We use non-perturbative linked-cluster expansions to determine the ground-state energy per site of the spin-one Heisenberg model on the kagome lattice. To this end, a parameter is introduced allowing to interpolate between a fully trimerized state and the isotropic model. The ground-state energy per site 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 the isotropic model which we attribute to divergencies of partial series in the graph expansion of quasi-1d unfrustrated chain graphs. More concretely, these divergencies can be traced back to a quantum critical point of the one-dimensional unfrustrated chain of coupled triangles. Interestingly, the reorganization of the non-perturbative linked-cluster expansion in terms of clusters with enhanced symmetry yields a ground-state energy per site of the isotropic two-dimensional model being in quantitative agreement with other numerical approaches in favor of a spontaneous trimerization of the system. Our findings are of general importance for any non-perturbative linked-cluster expansion on geometrically frustrated systems.

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D. Ixert, T. Tischler, K. P. Schmidt. 2015-08-21. Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model. https://doi.org/10.1103/physrevb.92.174422

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