Dynamical Mean-Field Theory of Resonating-Valence-Bond Antiferromagnets

We propose a theory of the spin dynamics of frustrated quantum antiferromagnets, which is based on an effective action for a plaquette embedded in a self-consistent bath. This approach, supplemented by a low-energy projection, is applied to the Kagomé antiferromagnet. We find that a spin-liquid regime extends to very low energy, in which local correlation functions have a slow decay in time, well described by power-law behavior and $\omega /T$ scaling of the response function: ${\chi }^{\prime \prime }\left(\omega \right)\propto {\omega }^{-\alpha }F(\omega /T)$.