  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 $\rho_{B}(\omega) \propto \omega^{s}$ 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.
