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We find the emergence of strong correlations and universality on the approachto the quantum critical points of a two impurity Anderson model. The twoimpurities are coupled by an inter-impurity exchange interaction $J$ and directinteraction $U_{12}$ and are hybridized with separate conduction channels.Thelow energy behavior is described in terms of renormalized parameters, which canbe deduced from numerical renormalization group (NRG) calculations. We showthat on the approach to the transitions to a local singlet and a local chargedordered state, the quasiparticle weight factor $z\to 0$, and the renormalizedparameters can be expressed in terms of a single energy scale $T^*$. The valuesof the renormalized interaction parameters in terms of $T^*$ can be predictedfrom the condition of continuity of the spin and charge susceptibilities, andcorrespond to strong correlation as they are greater than or equal to theeffective band width. These predictions are confirmed by the NRG calculations,including the case when the onsite interaction U=0.

Convergence of energy scales on the approach to a local quantum critical point