Kondo physics and dissipation: A numerical renormalization-group approach to Bose-Fermi Kondo models

TL;DR

This paper develops a numerical renormalization-group method to analyze Bose-Fermi Kondo models, revealing quantum critical points and phase transitions relevant to heavy-fermion systems and qubit devices.

Contribution

The authors extend the NRG method to treat BFKMs with arbitrary bath exponents, enabling detailed study of quantum criticality and phase transitions in these models.

Findings

Identified continuous quantum phase transition for 0<s<1 with hyperscaling and /T-scaling.

Discovered Kosterlitz-Thouless transition at s=1 for Ohmic dissipation.

Observed collapse of the Kondo resonance at the transition in impurity spectral functions.

Abstract

We extend the numerical renormalization-group method to treat Bose-Fermi Kondo models (BFKMs) describing a local moment coupled both to a conduction band and to a dissipative bosonic bath representing, e.g., lattice or spin collective excitations of the environment. We apply the method to the Ising-symmetry BFKM with a structureless band and a bath spectral function \eta(\omega)\propto \omega^s. The method is valid for all bath exponents s and all temperatures T. For 0<s<1, the range of interest in the context of heavy-fermion quantum criticality, an interacting critical point, characterized by hyperscaling of exponents and \omega/T-scaling, describes a continuous quantum phase transition between Kondo-screened and localized phases. For Ohmic dissipation s=1, where the model is relevant to certain dissipative mesoscopic qubit devices, the transition is found to be Kosterlitz-Thouless-like. In both regimes the impurity spectral function for the corresponding Anderson model shows clearly the collapse of the Kondo resonance at the transition. Connection is made to other recent results for the BFKM and the spin-boson model.