Phase boundaries of power-law Anderson and Kondo models: A poor man's scaling study

We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states rho(epsilon) proportional to | epsilon| (r), either vanishing (for r > 0) or diverging (for r < 0) at the Fermi energy epsilon = 0, that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., r > 0), we find the phase boundary for (a) 0 < r < 1/2, a range over which the model exhibits interacting quantum critical points both at and away from particle-hole (p-h) symmetry, and (b) r > 1, where the phases are separated by first-order quantum phase transitions that are accessible only for broken p-h symmetry. For the p-h-symmetric Kondo model with easy-axis or easy-plane anisotropy of the impurity-band spin exchange, the phase boundary and scaling trajectories are obtained for both r > 0 and r < 0. Throughout the regime of weak-to-moderate impurity-band coupling in which poor man's scaling is expected to be valid, the approach predicts phase boundaries in excellent qualitative and good quantitative agreement with the nonperturbative numerical renormalization group, while also establishing the functional relations between model parameters along these boundaries.