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

Abstract

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

5 pages 5 figures

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• Study of Hund's rule coupling in models of magnetic impurities and quantum dots
• Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
• Current cross-correlation in the Anderson impurity model with exchange interaction
• Bell-state correlations in current of local Fermi liquid