Two Channel Multi impurity Kondo model

We show that the Ruderman-Kittel-Kasua-Yoisida interaction between overscreened spins in two channel Kondo impurity systems is a relevant perturbation when the number of impurities N is greater than 3 driving the system to a new quantum critical point with anomalous dimensions $\frac{1}{ (N+1)}$ for the spin operator and the Sommerfeld coefficient of the specific heat scales as $\gamma \sim T^{- \frac{3}{N+1}}$. The critical point universal properties are relevant to many strong correlation problems, such as impurity placed in a Majorana metal and the multichannel Kondo lattice model of heavy fermion materials. We discuss relevance of our results for cluster DMFT studies of quantum criticality.