We have considered the competing effects of the electron-electron Hubbard repulsion and the electron-phonon interaction on the properties of a one-dimensional electron gas both within perturbation theory and by exact numerical solution of finite-length rings. We find that the perturbation-theory results provide a qualitatively correct description of the system over a considerable range of parameters. Among the more interesting conclusions we draw is that, so long as the repulsion $U$ is less than a critical value which depends on the strength of the electron-phonon interaction, the predictions of the Su-Schrieffer-Heeger model of polyacetylene are not profoundly affected by the electron-electron repulsion. A small splitting between the charged and neutral soliton-creation energies and minor shape changes are the principle effects.

• Received 21 October 1981

DOI:https://doi.org/10.1103/PhysRevB.26.4278