Low-energy sector of the S=1/2 Kagome antiferromagnet

Starting from a modified version of the S = 1/2 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.