Kondo Compensation in a Pseudogap Phase: a Renormalization Group Study

Abstract

We investigate the critical behavior of the Kondo compensation in the presence of a power-law pseudogap in the density of states, $\varrho (\ddot{I}‰)\sim |\ddot{I}‰{|}^{\hat{I}}\mu$. For $\hat{I}\mu <1$, 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 $\hat{I}º(j<j_c)=1-g(j)$ with the local $g$-factor vanishing as $g\sim |j-j_c{|}^2$. We combine perturbative drone fermion method with non-perturbative NRG computations to determine the critical exponent ${\hat{I}}^2(\hat{I}\mu )$, which exhibits a non-monotonous behavior as a function of $\hat{I}\mu$. Our results confirm that the Kondo cloud builds up continuously in the presence of a weak pseudogap as one approaches the phase transition.

8 pages, 8 figures