Renormalization group study of quantum criticality in gapped Kondo model

TL;DR

This study applies flow equation renormalization to the gapped Kondo model, revealing how increasing the gap suppresses Kondo screening and shifts the system towards a local moment fixed point, demonstrating local quantum criticality.

Contribution

First application of flow equation renormalization to the gapped Kondo model, showing how the gap influences quantum critical behavior and fixed points.

Findings

Kondo divergence is suppressed with increasing gap.

Susceptibility transitions to Curie behavior as gap increases.

Renormalization flow moves from strong coupling to local moment fixed point.

Abstract

Quantum impurity models are the prototypical examples of quantum many-body dynamics which manifests in their spectral and transport properties. Single channel Anderson(and Kondo model) leads to the Fermi liquid ground state in the strong coupling regime which corresponds to a stable infrared fixed point at which the quantum impurity gets completely screened by the conduction electrons. Quantum impurity models with non-trivial density of states exhibit quantum phase transition and this quantum criticality lies in the universality class of local quantum critical systems. In this paper, we report first study of the flow equation renormalization of gapped Kondo model which has gapped density of states, the gap being at the Fermi level. Flow equation renormalization group method has proved to be one of the very robust renormalization methods to study Kondo physics both in equilibrium as well as in non-equilibrium. Here we have shown that this method can also be employed to study local quantum criticality. We have calculated the flow equations for the Kondo coupling and solved them for various values of the gap parameter and we find that there is suppression of Kondo divergence as gap is increased which signifies that as gap is increased, renormalization flow goes away from the strong coupling fixed point. We have also calculated the spin susceptibility and we find that as gap is increased, susceptibility goes over to the Curie behaviour and hence confirming the renormalization flow towards the local moment fixed point.