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 kagome 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 a power law behaviour and $\omega/T$ scaling of the response function: $\chi''(\omega)\propto \omega^{-\alpha}F(\omega/T)$.