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We investigate quantum impurity problems, where a local magnetic moment iscoupled to the spin density of a bosonic environment, leading to bosonicversions of the standard Kondo and Anderson impurity models. In a physicalsituation, these bosonic environments can correspond either to deconfinedspinons in certain classes of Z_2 frustrated antiferromagnets, or to particlesin a multicomponent Bose gase (in which case the spin degree of freedom isattributed to hyperfine levels). Using renormalization group techniques, weestablish that our impurity models, which feature an exchange interactionanalogous to Kondo impurities in Fermi liquids, allow the flow towards a stablestrong-coupling state. Since the low-energy bosons live around a single pointin momentum space, and there is no Fermi surface, an impurity quantum phasetransition occurs at intermediate coupling, separating screened and unscreenedphases. This behavior is qualitatively different from previously studiedspin-isotropic variants of the spin-boson model, which display stableintermediate-coupling fixed points and no screening.Comment: 15 pages, 10 fig

Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths