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

TL;DR

This paper employs non-perturbative linked-cluster expansions to analyze the ground state of the spin-one Kagome Heisenberg model, revealing a spontaneous trimerization and addressing divergence issues near the isotropic point.

Contribution

It introduces a novel non-perturbative linked-cluster expansion method that effectively captures the ground state and trimerization in a frustrated quantum magnet.

Findings

Ground-state energy matches other numerical methods.

Evidence of spontaneous trimerization in the isotropic model.

Identification of quantum critical points affecting series convergence.

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.