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

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.

8 pages, 9 figures

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Cited by in corpus (8)

• Spin-S Kagome quantum antiferromagnets in a field with tensor networks
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Spin ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet
• Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems