  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.
