  Considering two non-interacting qubits in the context of open quantum
systems, it is well known that their common environment may act as an
entangling agent. In a perturbative regime the influence of the environment on
the system dynamics can effectively be described by a unitary and a dissipative
contribution. For the two-spin Boson model with (sub-) Ohmic spectral density
considered here, the particular unitary contribution (Lamb shift) easily
explains the buildup of entanglement between the two qubits. Furthermore it has
been argued that in the adiabatic limit, adding the so-called counterterm to
the microscopic model compensates the unitary influence of the environment and,
thus, inhibits the generation of entanglement. Investigating this assertion is
one of the main objectives of the work presented here. Using the hierarchy of
pure states (HOPS) method to numerically calculate the exact reduced dynamics,
we find and explain that the degree of inhibition crucially depends on the
parameter $s$ determining the low frequency power law behavior of the spectral
density $J(\omega) \sim \omega^s e^{-\omega/\omega_c}$. Remarkably, we find
that for resonant qubits, even in the adiabatic regime (arbitrarily large
$\omega_c$), the entanglement dynamics is still influenced by an
environmentally induced Hamiltonian interaction. Further, we study the model in
detail and present the exact entanglement dynamics for a wide range of coupling
strengths, distinguish between resonant and detuned qubits, as well as Ohmic
and deep sub-Ohmic environments. Notably, we find that in all cases the
asymptotic entanglement does not vanish and conjecture a linear relation
between the coupling strength and the asymptotic entanglement measured by means
of concurrence. Further we discuss the suitability of various perturbative
master equations for obtaining approximate entanglement dynamics.
