Exact solution for the general Peierls-Frohlich chain with disorder

Quasi-one-dimensional systems with arbitrary disorder that are subject to a Peierls (bond) or Frohlich (site) distortion can be classified in the continuum approximation by five parameters. These are bond and site gap, as well as forward, backward, and umklapp scattering. The averaged one-particle Green's function of the general continuum model is calculated exactly by means of the supersymmetry method. The density of states and the localization length are given by an explicit formula in terms of the hypergeometric function. The results are applied to discuss the tail in the optical conductivity of polyacetylene and to investigate the combined influence of site and bond gaps in diatomic chains.