Recent studies of the global phase diagram of quantum-critical heavy-fermion metals prompt consideration of the interplay between the Kondo interactions and quantum fluctuations of the local moments alone. Toward this goal, we study a Bose-Fermi Kondo model (BFKM) with Ising anisotropy in the presence of a local transverse field that generates quantum fluctuations in the local-moment sector. We apply the numerical renormalization-group method to the case of a sub-Ohmic bosonic bath exponent and a constant conduction-electron density of states. Starting in the Kondo phase at zero transverse-field, there is a smooth crossover with increasing transverse field from a fully screened to a fully polarized impurity spin. By contrast, if the system starts in its localized phase, then increasing the transverse field causes a continuous, Kondo-destruction transition into the partially polarized Kondo phase. The critical exponents at this quantum phase transition exhibit hyperscaling and take essentially the same values as those of the BFKM in zero transverse field. The many-body spectrum at criticality varies continuously with the bare transverse field, indicating a line of critical points. We discuss implications of these results for the global phase diagram of the Kondo lattice model.
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