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We analyze the static and dynamical properties of two Ising-coupled quantumspins embedded in a common bosonic bath as an archetype of dissipative quantummechanics. First, we elucidate the ground state phase diagram for an ohmic anda subohmic bath using a combination of bosonic numerical renormalization group(NRG), analytical techniques and intuitive arguments. Second, employing thetime-dependent NRG we investigate the system's rich dynamical behavior arisingfrom the complex interplay between spin-spin and spin-bath interactions.Interestingly, spin oscillations can synchronize due to the proximity of thecommon non-Markovian bath and the system displays highly entangled steadystates for certain nonequilibrium initial preparations. We complement ournon-perturbative numerical results by exact analytical solutions when availableand provide quantitative limits on the applicability of the perturbativeBloch-Redfield approach at weak coupling.

Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins