Spin-boson coupling in continuous-time quantum Monte Carlo

A vector bosonic field coupled to the electronic spin is treated by means of the continuous-time quantum Monte Carlo method. In the Bose-Kondo model with a sub-Ohmic density of states ρ_B(ω)ωs with s=0.2, two contributions to the spin susceptibility, the Curie term T^-1 and the term T^-s due to bosonic fluctuations, are observed separately. This result indicates the existence of a residual moment and a hidden critical behavior. By including hybridization with itinerant electrons, a quantum critical point is identified between this local-moment state and the Kondo singlet state. It is demonstrated that the energy scale of the bosonic fluctuations is not affected by the quantum phase transition.