  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.
