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Two-bath spin-boson model: Phase diagram and critical properties

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.