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

TL;DR

This paper investigates the universal behavior and strong correlations near quantum critical points in a two impurity Anderson model, revealing how renormalized parameters and energy scales characterize the transition to local singlet and charge-ordered states.

Contribution

It introduces a unified description of low-energy behavior using a single energy scale and confirms predictions with numerical renormalization group calculations, even at zero onsite interaction.

Findings

Quasiparticle weight z approaches zero near critical points

Renormalized parameters are expressed in terms of a single energy scale T*

Predictions confirmed by NRG calculations, including U=0 case

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 $T^*$. The values of the renormalized interaction parameters in terms of $T^*$ 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.