Kondo Compensation in a Pseudogap Phase: a Renormalization Group Study

We investigate the critical behavior of the Kondo compensation in the presence of a power-law pseudogap in the density of states, $\varrho(\omega)\sim |\omega|^\epsilon$. For $\epsilon<1$, this model exhibits a quantum phase transition from a partially screened doublet ground state to a fully screened many-body singlet ground state with increasing Kondo coupling, $j$. At the critical point, $j_c$, the Kondo compensation is found to scale as $\kappa(j<j_c) = 1- g(j)$ with the local $g$-factor vanishing as $g \sim |j-j_c|^\beta$. We combine perturbative drone fermion method with non-perturbative NRG computations to determine the critical exponent $\beta (\epsilon)$, which exhibits a non-monotonous behavior as a function of $\epsilon$. Our results confirm that the Kondo cloud builds up continuously in the presence of a weak pseudogap as one approaches the phase transition.