  The spin-boson model, describing a two-level system coupled to a bath of
harmonic oscillators, is a generic model for quantum dissipation, with manifold
applications. It has also been studied as a simple example for an impurity
quantum phase transition. Here we present a detailed study of a U(1)-symmetric
two-bath spin-boson model, where two different components of an SU(2) spin 1/2
are coupled to separate dissipative baths. Non-trivial physics arises from the
competition of the two dissipation channels, resulting in a variety of phases
and quantum phase transitions. We employ a combination of analytical and
numerical techniques to determine the properties of both the stable phases and
the quantum critical points. In particular, we find a critical
intermediate-coupling phase which is bounded by a continuous quantum phase
transition which violates the quantum-to-classical correspondence.
