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