Quantum lattice fluctuations in nearly degenerate quasi one-dimensional polymers

It has been shown that the linear and nonlinear optical behaviors are quite different for degenerate and nondegenerate polymers. Quantum lattice fluctuations are believed to play an important role in the understanding of these optical properties. In this work, we study the quantum lattice fluctuations in a nondegenerate conjugated polymer by means of a modified Su-Schrieffer-Heeger-type model Hamiltonian. We first integrate out the electronic variables of the partition function and obtain an effective phonon action. Then an equation for the phonon order parameter is derived within a one-loop approximation. We find that the quantum lattice fluctuations is reduced by the nondegenerate ground state, especially in the weak electron-phonon coupling. This result is compatible with the optical properties of degenerate and nondegenerate polymers.