Quantum phase transitions in the Bose-Fermi Kondo model

TL;DR

This paper investigates quantum phase transitions in the Bose-Fermi Kondo model, analyzing fixed points and anisotropy effects, with implications for quantum criticality and dynamical mean field theory.

Contribution

It introduces a second order expansion method to analyze fixed points and reveals the relevance of anisotropy at non Fermi liquid fixed points.

Findings

Anisotropy influences the nature of quantum phase transitions.

Derived an exact relation between anomalous exponents.

Identified the dominant fixed points governing the transitions.

Abstract

We study quantum phase transitions in the Bose-Fermi Kondo problem, where a local spin is coupled to independent bosonic and fermionic degrees of freedom. Applying a second order expansion in the anomalous dimension of the Bose field we analyze the various non-trivial fixed points of this model. We show that anisotropy in the couplings is relevant at the SU(2) invariant non Fermi liquid fixed points studied earlier and thus the quantum phase transition is usually governed by XY or Ising-type fixed points. We furthermore derive an exact result that relates the anomalous exponent of the Bose field to that of the susceptibility at any finite coupling fixed point. Implications on the dynamical mean field approach to locally quantum critical phase transitions are also discussed.