Kondo Compensation in a Pseudogap Phase: a Renormalization Group Study

TL;DR

This study explores the quantum phase transition of Kondo screening in a pseudogap environment, revealing how the critical behavior and exponents depend on the pseudogap exponent using RG and NRG methods.

Contribution

It combines perturbative and non-perturbative techniques to determine the critical exponent for Kondo compensation in a pseudogap phase, revealing non-monotonous behavior.

Findings

Kondo phase transition occurs at a critical coupling $j_c$ for $ ext{epsilon}<1$

The local $g$-factor vanishes as $g o 0$ near the critical point with a specific exponent

The critical exponent $eta( ext{epsilon})$ varies non-monotonously with $ ext{epsilon}$

Abstract

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