  This work addresses quantum adiabatic decoherence of many-body spin systems
coupled with a boson field in the framework of open quantum systems theory. We
generalize the traditional spin-boson model by considering a system-environment
interaction Hamiltonian that represents a partition of non-interacting
subsystems and highlights the collective correlation that appears exclusively
due to the coupling with a common environment. Remarkably, this simple, exactly
solvable model encompasses relevant aspects of a many-body open quantum system
and features the subtle quantum effects that arise when the size scales up to a
macroscopic level. We derive an analytical expression for the time dependence
of the density matrix without assuming coarse-graining. The resulting
decoherence function is eigen-selective and is a complex exponential whose
exponent has a real part that introduces a decay similar to that in the
spin-boson model. On the contrary, the imaginary part depends on the quantum
numbers and geometry of the whole partition and does not reflect the system
temperature. Motivated by decoherence in solid-state NMR we apply the
theoretical results to a partition of dipole-coupled spin pairs in contact with
a common phonon bath, using typical parameters of hydrated salts. The proposal
allows estimating the decoherence time scale in terms of the system physical
constants. As a significant novelty, the decoherence function phase depends on
the eigenvalue distribution throughout the sample. It plays the leading role,
overshadowing the mechanism associated with the bath thermal state. Finally, we
apply the formalism to describe decoherence in the "magic echo" NMR reversal
experiment. We find that the system-environment correlation explains the origin
of irreversibility, and both the decoherence rate value and its dependence on
the dipolar frequency, are remarkably similar to the experiment.
