The Kondo effect revisited: RG-improved perturbation theory based on the Schwinger-boson representation

TL;DR

This paper develops an RG-improved perturbation theory using Schwinger-boson representation to describe the Kondo effect across all temperature regimes, connecting weak and strong coupling states.

Contribution

It introduces a novel RG-improved perturbation approach based on Schwinger-bosons that captures the entire temperature range of the Kondo effect, including the strong coupling fixed point.

Findings

Successfully describes the crossover from local moment to Fermi-liquid state

Accesses the strong coupling fixed point perturbatively

Suggests spinon statistics are determined by system dynamics

Abstract

Resorting to the Schwinger-boson representation for the description of a localized magnetic-impurity state, we develop an RG-improved (renormalization group) perturbation theory for the Kondo effect. This Schwinger-boson based RG-improved perturbation theory covers the whole temperature range from a decoupled local moment state to a local Fermi-liquid state through the crossover temperature regime, shown from the specific heat and spin susceptibility of the magnetic impurity. The Schwinger-boson based RG-improved perturbation theory makes the strong coupling fixed point at IR (infrared) accessible from the gaussian one at UV (ultraviolet) within the perturbation framework, regarded to be complementary to the Schwinger-boson based NCA (non-crossing approximation) self-consistent theory [Phys. Rev. Lett. {\bf 96}, 016601 (2006)]. The existence of the perturbatively accessible strong coupling fixed point implies the nature on the statistics of spinons, not determined by hands but chosen by the nature of strongly coupled systems.