  We determine the conditions under which general dimer-type spin chains with
$XYZ$ couplings of arbitrary range in a general transverse field will exhibit
an exactly separable parity-breaking eigenstate. We also provide sufficient
conditions which ensure that it will be a ground state. We then examine the
exact side limits at separability of the entanglement between any two spins in
a finite chain, showing that in the vicinity of separability, the system will
loose all signatures of dimerization, with pairwise entanglement approaching
infinite range and becoming independent of separation and interaction range.
The possibility of a non-uniform exactly separable ground state induced by an
alternating field is also shown. As illustration, we examine the behavior of
the pairwise entanglement in a finite $XY$ dimer chain under a uniform as well
as alternating field. Related aspects of the magnetization are also discussed.

Quantum Physics