Abstract
In this work we investigate charge transport in one-dimensional insulators via semiclassical and perturbative renormalization group methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that nonlinear collective modes such as polarons and solitons are responsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss fhe differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.