By using a simple model of soliton-antisoliton pairs to simulate the quantum lattice fluctuations in one-dimensional organic polymers, in which the subgap absorption results from the transitions between the lowest unoccupied and the highest occupied levels off the conduction and valence bands, respectively, in the soliton-antisoliton excitations. There is no gap in the absorption. Our result indicates clearly that the nondegeneracy of ground-states suppresses the quantum fluctuations, so that the subgap absorption is reduced and there is a related clear onset in the absorption spectrum of nondegenerate polymers, which is in agreement with experiments.