  The search of new means of generating and controlling topological states of
matter is at the front of many joint efforts, including bandgap engineering by
doping and light-induced topological states. Most of our understading, however,
is based on a single particle picture. Topological states in systems including
interaction effects, such as electron-electron and electron-phonon, remain less
explored. By exploiting a non-perturbative and non-adiabatic picture, here we
show how the interaction between electrons and a coherent phonon mode can lead
to a bandgap hosting edge states of topological origin. Further numerical
simulations witness the robustness of these states against different types of
disorder. Our results contribute to the search of topological states, in this
case in a minimal Fock space.
