Numerical renormalization-group study of the Bose-Fermi Kondo model

TL;DR

This paper develops a numerical renormalization-group approach for Bose-Fermi Kondo models, revealing a quantum critical point with hyperscaling and $mbda/T$-scaling, relevant for heavy-fermion systems.

Contribution

The authors extend the NRG method to Bose-Fermi Kondo models, enabling detailed analysis of quantum criticality in systems with both fermionic and bosonic baths.

Findings

Identification of an interacting critical point for 0<s<1

Observation of hyperscaling of exponents at the critical point

Demonstration of mbda/T-scaling behavior in the model

Abstract

We extend the numerical renormalization-group method to Bose-Fermi Kondo models (BFKMs), describing a local moment coupled to a conduction band and a dissipative bosonic bath. We apply the method to the Ising-symmetry BFKM with a bosonic bath spectral function $\eta(\omega)\propto \omega^s$, of interest in connection with heavy-fermion criticality. For $0<s<1$, an interacting critical point, characterized by hyperscaling of exponents and $\omega/T$-scaling, describes a quantum phase transition between Kondo-screened and localized phases. Connection is made to other results for the BFKM and the spin-boson model.