Quantum critical properties of the Bose-Fermi Kondo Model in a large-N limit

TL;DR

This paper investigates the quantum critical behavior of the Bose-Fermi Kondo model using a large-N approach, revealing an unstable fixed point, diverging susceptibility, and extended /T scaling that challenges classical mappings.

Contribution

The study introduces a dynamical large-N analysis of a generalized Bose-Fermi Kondo model, identifying a quantum critical point with unique scaling properties and an unstable fixed point.

Findings

Existence of an unstable fixed point for sub-ohmic baths.

Divergence of local spin susceptibility at the quantum critical point.

Extended /T scaling over 15 decades, indicating quantum nature of the critical point.

Abstract

Studies of non-Fermi liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large-N approach to analyze an SU(N)xSU($\kappa N$) generalization of the model. We establish the existence in this limit of an unstable fixed point when the bosonic bath has a sub-ohmic spectrum ($|\omega|^{1-\epsilon} \sgn \omega$, with $0<\epsilon<1$). At the quantum critical point, the Kondo scale vanishes and the local spin susceptibility (which is finite on the Kondo side for \kappa <1) diverges. We also find an \omega/T scaling for an extended range (15 decades) of \omega/T. This scaling violates (for $\epsilon \ge 1/2$) the expectation of a naive mapping to certain classical models in an extra dimension; it reflects the inherent quantum nature of the critical point.