  The effects of quantum lattice fluctuations on the Peierls transition and the
optical conductivity in the one-dimensional Holstein model of spinless fermions
have been studied by developing an analytical approach, based on the unitary
transformation method. We show that when the electron-phonon coupling constant
decreases to a finite critical value the Peierls dimerization is destroyed by
the quantum lattice fluctuations. The dimerization gap is much more reduced by
the quantum lattice fluctuations than the phonon order parameter. The
calculated optical conductivity does not have the inverse-square-root
singularity but have a peak above the gap edge and there exists a significant
tail below the peak. The peak of optical-conductivity spectrum is not directly
corresponding to the dimerized gap. Our results of the phase diagram and the
spectral-weight function agree with those of the density matrix renormalization
group and the exact diagonalization methods.
