Breakdown of the adiabatic approximation in trans-polyacetylene

We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalization group method. The model is parametrized for trans-polyacetylene. We calculate the ground state and first excited odd-parity singlet and triplet states. We investigate their energies and geometries for up to 102 sites. The transition energy and the soliton width of the triplet state show significant deviations from the adiabatic approximation for chain lengths larger than the classical soliton size. In contrast, the transition energy of the singlet is close to the adiabatic prediction