We consider the finite-temperature scaling properties of a Kondo-destroying quantum critical point in the Ising-anisotropic Bose-Fermi Kondo model (BFKM). A cluster-updating Monte Carlo approach is used, in order to reliably access a wide temperature range. The scaling function for the two-point spin correlator is found to have the form dictated by a boundary conformal field theory, even though the underlying Hamiltonian lacks conformal invariance. Similar conclusions are reached for all multipoint correlators of the spin-isotropic BFKM in a dynamical large-N limit. Our results suggest that the quantum critical local properties of the sub-Ohmic BFKM are those of an underlying boundary conformal field theory.
Studies of non-Fermi-liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large-
N approach to analyze an $\mathrm{S}\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{S}\mathrm{U}(\ensuremath{\kappa}N)$ generalization of the model. We establish the existence in this limit of an unstable fixed point when the bosonic bath has a sub-Ohmic spectrum ($|\ensuremath{\omega}{|}^{1\ensuremath{-}ϵ}\mathrm{s}\mathrm{g}\mathrm{n}\ensuremath{\omega}$, with
0<ϵ<1). At the quantum-critical point, the Kondo scale vanishes and the local spin susceptibility (which is finite on the Kondo side for $\ensuremath{\kappa}<1$) diverges. We also find an $\ensuremath{\omega}/T$ scaling for an extended range (15 decades) of $\ensuremath{\omega}/T$. This scaling violates (for $ϵ\ensuremath{\ge}1/2$) the expectation of a naive mapping to certain classical models in an extra dimension; it reflects the inherent quantum nature of the critical point.
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 ${|\ensuremath{\epsilon}|}^{r}$ at the Fermi energy ($\ensuremath{\epsilon}=0$) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to ${|\ensuremath{\omega}|}^{s}$. 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<21 and $\frac{1}{2}\ensuremath{\le}s<1$, 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 $\ensuremath{\omega}/T$ 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.