Coherence scale of coupled Anderson impurities

For two coupled Anderson impurities, two energy scales are present to characterize the evolution from the local moment state of the impurities to either the interimpurity singlet or the Kondo singlet ground state. The high-energy scale is found to deviate from the single-ion Kondo temperature and rather scales as the Ruderman-Kittel-Kasuya-Yosida interaction when it becomes dominant. We find that the scaling behavior and the associated physical properties of this scale are consistent with those of a coherence scale defined in heavy fermion systems.