  The quantistic zero-point motion of the carbon atoms is shown to induce
strong effects on the opto-electronic properties of diamond and
trans-polyacetylene, a conjugated polymer. By using an ab initio approach, we
interpret the sub-gap states experimentally observed in diamond in terms of
entangled electron-phonon states. These states also appear in
trans-polyacetylene causing the formation of strong structures in the
band-structure that even call into question the accuracy of the band theory.
This imposes a critical revision of the results obtained for carbon-based
nano-structures by assuming the atoms frozen in their equilibrium positions.
