Nonperturbative linked-cluster expansions for the trimerized ground state of the spin-one kagome Heisenberg model

• Published in: Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2015-11, Vol.92 (17), Article 174422
• Main Authors: Ixert, Dominik, Tischler, Tobias, Schmidt, Kai P.
• Format: Article
• Language: English
• Subjects: Chains; Clusters; Condensed matter; Graphs; Ground state; Mathematical models; Spontaneous; Triangles
• ISSN: 1098-0121; 1550-235X
• DOI: 10.1103/PhysRevB.92.174422

We use nonperturbative 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 us 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 behavior 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 nonperturbative linked-cluster expansion in terms of clusters with enhanced symmetry yields a ground-state energy per site of the isotropic two-dimensional model that is in quantitative agreement with other numerical approaches in favor of a spontaneous trimerization of the system. Our findings are of general importance for any nonperturbative linked-cluster expansion on geometrically frustrated systems.