  We study the metal-insulator transition in a very general two-channel
transport model, where charge carriers are coupled to a correlated background
medium. The fluctuations of the background were described as bosonic
excitations, having the ability to relax. Employing an analytical
projector-based renormalization technique, we calculate the ground-state and
spectral properties of this fermion-boson model and corroborate recent
numerical results, which indicate---in dependence on the `stiffness' of the
background medium---a Luttinger-liquid to charge-density-wave transition for
the one-dimensional half-filled band case. In particular, we determine the
renormalized electron and boson dispersion relations and show that the quantum
phase transition is not triggered by a softening of the boson modes. Thus the
charge density wave is different in nature from an usual Peierls distorted
state.
