Correlations between two Anderson impurities

We study the intersite correlation effects on the Kondo dynamics of two Anderson impurities. Two characteristic energy scales are present associated with the splitting of the uniform and staggered spin susceptibilities. The high energy scale has similar properties as the coherence scale in heavy fermion materials while the low energy scale characterizes the competing orders between Kondo singlet state and inter-impurity singlet state. A singlet superconductivity instability is found near the quantum critical point and is associated with the singular staggered spin susceptibility.