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

Abstract

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 ρ(ε) ∝ |ε| r , either vanishing (for r > 0) or diverging (for r < 0) at the Fermi energy ε = 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.

Reentrant Kondo effect in a quantum impurity coupled to a metal-semiconductor hybrid contact

“…We can write this result in another way. Defining ρ ′ 0 = D r ρ 0 , we can show that 2ρ ′ 0 J C = r, and this result is already known in the literature for pseudo-gap systems [see [32] for more details about this system].…”

“…In particular, it is known that Eq. (4.14) is unable to describe correctly the physical regimes ifΓ > Λ >Ũ /2 [32], however it shows thatŨ rapidly decreases with Λ.…”

“…Following Cheng et al [32], we perform a poor man's scaling calculation on our H SIAM . Application of the poor man's scaling to Anderson Model is similar but has small differences than the Poor man's scaling calculations to the Kondo model.…”

“…The advantage, however, is that within the Kondo model we can employ more easily the scaling analysis, a technique that allows us to obtain some relevant physical quantities of the problem, such as the Kondo temperature [31]. In some particular case it is also instructive to apply scaling analysis in Andereson Model [32]. Despite the usefulness of the many approximation solutions for the Anderson and Kondo models, they fail to properly describe the ground state of the system.…”

“…For instance, in pseudo-gap systems, in which the conduction band density ρ(ε) of states depends on the energy ε as ε r , with 0 < r < 2, there is a critical Kondo coupling below which there is no screening [37]. Also working with pseudo-gap system, Cheng et al [32] found the SIAM fixed points using poor man's scaling in Anderson Model.…”