  We investigate quantum impurity problems, where a local magnetic moment is
coupled to the spin density of a bosonic environment, leading to bosonic
versions of the standard Kondo and Anderson impurity models. In a physical
situation, these bosonic environments can correspond either to deconfined
spinons in certain classes of Z_2 frustrated antiferromagnets, or to particles
in a multicomponent Bose gase (in which case the spin degree of freedom is
attributed to hyperfine levels). Using renormalization group techniques, we
establish that our impurity models, which feature an exchange interaction
analogous to Kondo impurities in Fermi liquids, allow the flow towards a stable
strong-coupling state. Since the low-energy bosons live around a single point
in momentum space, and there is no Fermi surface, an impurity quantum phase
transition occurs at intermediate coupling, separating screened and unscreened
phases. This behavior is qualitatively different from previously studied
spin-isotropic variants of the spin-boson model, which display stable
intermediate-coupling fixed points and no screening.
