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

摘要

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