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, $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\sim}{|\ensuremath{\omega}|}^{\ensuremath{\epsilon}}$. For $\ensuremath{\epsilon}<1$, generically---in the absence of particle-hole symmetry---this model exhibits a quantum phase transition from a partially screened doublet ground state to a fully screened many-body ground state upon increasing the exchange coupling $j$. At the critical point ${j}_{\text{c}}$, the Kondo compensation is found to scale as $\ensuremath{\kappa}(j<{j}_{\text{c}})=1\ensuremath{-}g(j)$ with the local $g$-factor vanishing as $g\ensuremath{\sim}|j\ensuremath{-}{j}_{\text{c}}{|}^{\ensuremath{\beta}}$. We combine the perturbative drone fermion method with the nonperturbative numerical renormalization group computations to determine the critical exponent $\ensuremath{\beta}(\ensuremath{\epsilon})$, which exhibits a nonmonotonous behavior as a function of $\ensuremath{\epsilon}$. Our results confirm that the Kondo cloud builds up continuously in the presence of a weak pseudogap as one approaches the phase transition.