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We address the phenomenon of critical Kondo destruction in pseudogapBose-Fermi Anderson and Kondo quantum impurity models. These models describe alocalized level coupled both to a fermionic bath having a density of statesthat vanishes like |\epsilon|^r at the Fermi energy (\epsilon=0) and, via onecomponent of the impurity spin, to a bosonic bath having a sub-Ohmic spectraldensity proportional to |\omega|^s. Each bath is capable by itself ofsuppressing the Kondo effect at a continuous quantum phase transition. We studythe interplay between these two mechanisms for Kondo destruction usingcontinuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson modelwith 0<r<1/2 and 1/2<s<1, and applying the numerical renormalization-group tothe corresponding Kondo model. At particle-hole symmetry, the models exhibit aquantum critical point between a Kondo (fermionic strong-coupling) phase and alocalized (Kondo-destroyed) phase. The two solution methods, which are in goodagreement in their domain of overlap, provide access to the many-body spectrum,as well as to correlation functions including, in particular, thesingle-particle Green's function and the static and dynamical local spinsusceptibilities. The quantum-critical regime exhibits the hyperscaling ofcritical exponents and \omega/T scaling in the dynamics that characterize aninteracting critical point. The (r,s) plane can be divided into three regions:one each in which the calculated critical properties are dominated by thebosonic bath alone or by the fermionic bath alone, and between these tworegions, a third in which the bosonic bath governs the critical spin responsebut both baths influence the renormalization-group flow near the quantumcritical point.

Quantum criticality in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction