  The coexistence in the low-temperature spin-conducting phases of the zigzag
materials BaCo2V2O8 and SrCo2V2O8 of one-dimensional (1D) physics with
important deviations from it is not well understood. The studies of this paper
account for an important selection rule that follows from interchain spin
states being coupled more strongly within the spin dynamical structure factor
of such zigzag materials whenever they are connected by a specific symmetry
operation of the underlying lattice. In the case of excited states, this
symmetry operation is only a symmetry in spin-space ifno electronic spin flip
is performed within the generation of such states. Our results on both the role
of selective interchain couplings in protecting the 1D physics and being behind
deviations from it and on the dynamical properties being controlled by
scattering of singlet pairs of physical spins 1/2 open the door to a key
advance in the understanding of the physics of the spin chains in BaCo2V2O8 and
SrCo2V2O8.
