Study of Low-energy States of Clusters of Spin-1/2 and Spin-1 Triangles with Kagome-like Geometries

TL;DR

This study investigates the low-energy excitations of spin-1/2 and spin-1 antiferromagnetic clusters with Kagome-like and sawtooth geometries, revealing how geometry and spin influence excitation gaps and states.

Contribution

It provides a comparative analysis of low-energy states in different geometries and spin configurations, highlighting the impact of lattice structure on excitation spectra.

Findings

Kagome clusters with spin-1 sites have gapped singlet and triplet excitations.

Kagome clusters with spin-1/2 sites exhibit multiple low-energy singlet states, possibly gapless.

Sawtooth chains with spin-1 sites have gapped triplet excitations, with singlet gaps about twice the triplet gap.

Abstract

We study the low-energy properties of Heisenberg antiferromagnetic spin-1/2 and spin-1 systems on various clusters made up of triangles. Some of the clusters have a geometry similar to representative pieces of the Kagome lattice, while others have the geometry of a sawtooth chain. While the ground state always has the lowest possible spin (0 or 1/2), the nature of the low-energy excitations depends on the geometry and the site spin. For the Kagome clusters with spin-1 sites, the lowest excitations are gapped, with singlet and triplet excitations having similar gaps. This is in contrast to Kagome clusters with spin-1/2 sites where there are several low-energy singlet excitations (possibly gapless in the thermodynamic limit), while triplet excitations have a gap. For the sawtooth chain with spin-1 sites, the lowest excitations are triplets with a gap; the gap to singlet excitations is about twice the triplet gap.