Critical local moment fluctuations in the Bose-Fermi Kondo model

TL;DR

This paper analyzes the critical behavior of the Bose-Fermi Kondo model, revealing an unstable fixed point with critical local moment fluctuations and demonstrating the robustness of locally critical quantum phase transitions.

Contribution

It extends the understanding of the Bose-Fermi Kondo model by performing higher-order epsilon-expansion and identifying a universal critical exponent for local spin susceptibility.

Findings

Unstable fixed point identified in both isotropic and anisotropic cases.

Critical local spin susceptibility exponent equals epsilon.

Supports the robustness of locally critical quantum phase transitions in Kondo lattices.

Abstract

We consider the critical properties of the Bose-Fermi Kondo model, which describes a local moment simultaneously coupled to a conduction electron band and a fluctuating magnetic field, i.e., a dissipative bath of vector bosons. We carry out an $\epsilon-$expansion to higher than linear orders. (Here $\epsilon$ is defined in terms of the power-law exponent of the bosonic-bath spectral function.) An unstable fixed point is identified not only in the spin-isotropic case but also in the presence of anisotropy. It marks the point where the weight of the Kondo resonance has just gone to zero, and the local moment fluctuations are critical. The exponent for the local spin susceptibility at this critical point is found to be equal to $\epsilon$ in all cases. Our results imply that a quantum phase transition of the ``locally critical'' type is a robust microscopic solution to Kondo lattices.