  We have studied the interplay of a local phonon mode embedded in a metallic
host (Holstein impurity model) using Abelian bosonization. The phonon frequency
softens, which takes place in two steps: first, their frequency starts
softening, and acquires finite lifetime. Then oscillations disappear from the
response, and two distinct, finite dampings characterize them. Similar
behaviour shows up in the spin-boson model. Due to phonons, the electrons
experience an attractive, dynamic interaction. As a result, the electronic
charge response enhances similarly to the spin response in the Kondo model. The
local electronic density of states develops a dip around zero frequency. Thus
the chance of charge-Kondo effect emerges.
