  An analytical nonadiabatic approach has been developed to study the
dimerization gap and the optical absorption coefficient of the
Su-Schrieffer-Heeger model where the electrons interact with dispersive quantum
phonons. By investigating quantitatively the effects of quantum phonon
fluctuations on the gap order and the optical responses in this system, we show
that the dimerization gap is much more reduced by the quantum lattice
fluctuations than the optical absorption coefficient is. The calculated optical
absorption coefficient and the density of states do not have the
inverse-square-root singularity, but have a peak above the gap edge and there
exist a significant tail below the peak. The peak of optical absorption
spectrum is not directly corresponding to the dimerized gap. Our results of the
optical absorption coefficient agree well with those of the experiments in both
the shape and the peak position of the optical absorption spectrum.
