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Abstract

We address the phenomenon of critical Kondo destruction in pseudogap Bose- Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like | is an element of | r at the Fermi energy (is an element of = 0) and, via one component of the impurity spin, to a bosonic bath having a sub- Ohmic spectral density proportional to |omega|(s). Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous- time quantum Monte Carlo for the pseudogap Bose- Fermi Anderson model with 0 < r < 1/2 and 1/2 s < 1, and applying the numerical renormalization group to the corresponding Kondo model. At particle- hole symmetry, the models exhibit a quantum- critical point between a Kondo (fermionic strong- coupling) phase and a localized (Kondo- destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many- body spectrum, as well as to correlation functions including, in particular, the single- particle Green's function and the static and dynamical local spin susceptibilities. The quantum- critical regime exhibits the hyperscaling of critical exponents and omega/T scaling in the dynamics that characterize an interacting critical point. The (r, s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization- group flow near the quantum- critical point.