Low-Energy Sector of theS=1/2Kagome Antiferromagnet

Abstract

Starting from a modified version of the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ 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.