Low-Energy Sector of the $\mathit{S}\mathit{}=1\mathrm{}/2$ Kagome Antiferromagnet

Starting from a modified version of the $S=1/2\mathrm{}$ Kagome antiferromagnet to emphasize the role of elementary triangles, an effective Hamiltonian involving spin and chirality variables is derived. A mean-field decoupling that retains the quantum nature of these variables is shown to yield a Hamiltonian that can be solved exactly, leading to the following predictions: (i) The number of low-lying singlet states increases with the number of sites $N$ like ${1.15}^N$; (ii) a singlet-triplet gap remains in the thermodynamic limit; (iii) spinons form bound states with a small binding energy. By comparing these properties with those of the regular Kagome lattice as revealed by numerical experiments, we argue that this description captures the essential low-energy physics of that model.