Effect of Quantised Lattice Fluctuations on the Electronic States of Polyenes

We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalisation group method. The model is parametrised for polyenes. We calculate the ground state, and first excited odd-parity singlet and triplet states; and we investigate their energies, and bond length changes and fluctuations for up to 30 sites. The transition energy and the soliton width of the triplet state show deviations from the adiabatic approximation for chain lengths larger than the classical soliton size, because of de-pinning by the quantised lattice fluctuations.