The quantum zero-point motion of the carbon atoms is shown to induce strong effects on the optical and electronic properties of diamond and trans-polyacetylene, a conjugated polymer. By using an ab initio approach, we interpret the subgap 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 nanostructures by assuming the atoms frozen in their equilibrium positions.
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