  In this work we investigate charge transport in one-dimensional (1D)
insulators via semi-classical and perturbative renormalization group (RG)
methods. We consider the problem of electron-electron, electron-phonon and
electron-two-level system interactions. We show that non-linear collective
modes such as polarons and solitons are reponsible for transport. We find a new
excitation in the Mott insulator: the polaronic soliton. We discuss the
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.
