Study of Hund's rule coupling in models of magnetic impurities and quantum dots

Studies of the effects of the Hund's rule coupling J_H in multiple orbit impurities or quantum dots using different models have led to quite different predictions for the Kondo temperature T_K as a function of J_H. We show that the differences depend on whether or not the models conserve orbital angular momentum about the impurity site. Using numerical renormalization group (NRG) calculations, we deduce the renormalized parameters for the Fermi liquid regime, and show that, despite the differences between the models, the low energy fixed point in the strong correlation regime is universal with a single energy scale T_K, and just two renormalized interaction parameters, a renormalized single orbital term, U = 4T_K, and renormalized Hund's rule term, J_H = 8T_K/3.