We study the problem of one-dimensional (1D) Luttinger liquids in the insulating Mott-Hubbard phase in the presence of acoustic phonons in the semiclassical limit. We show that solitonic excitations can propagate freely in the system and the energy required to produce a soliton is reduced by a polaronic effect. We find a critical value of the electron-phonon coupling constant for which this energy vanishes.
@article{arxiv.cond-mat/0010497,
title = {Phonons and Solitons in 1D Mott Insulators},
author = {Chun-Min Chang and A. H. Castro Neto and A. R. Bishop},
journal= {arXiv preprint arXiv:cond-mat/0010497},
year = {2009}
}