Two-channel pseudogap Kondo and Anderson models: Quantum phase transitions and non-Fermi liquids

TL;DR

This paper investigates the quantum phase transitions and non-Fermi liquid behavior in two-channel pseudogap Kondo and Anderson models using analytical and numerical methods, revealing new stable fixed points and critical phenomena.

Contribution

It introduces a comprehensive analysis of impurity phases and quantum phase transitions in pseudogap Kondo models, including new fixed points and field theories formulated in fermionic variables.

Findings

Stable non-Fermi liquid phase exists for 0<r<0.23.

Critical fixed point with emergent symmetry appears for r>0.23.

Analytical results agree with numerical renormalization group data.

Abstract

We discuss the two-channel Kondo problem with a pseudogap density of states, $\rho(\w)\propto|\w|^r$, of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic $r=0$ case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for $0<r<\rmax\approx0.23$. For $r>\rmax$, this non-Fermi liquid phase disappears, and instead a critical fixed point with an emergent spin--channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose low-energy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions $r=0$ and $r=1$, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.