  Certain periodically driven quantum many-particle systems in one dimension
are known to exhibit edge modes that are related to topological properties and
lead to approximate degeneracies of the Floquet spectrum. A similar situation
occurs in spin chains, where stable edge modes were shown to exist at all
energies in certain integrable spin chains. Moreover, these edge modes were
found to be remarkably stable to perturbations. Here we investigate the
stability of edge modes in interacting, periodically driven, clean systems. We
introduce a model that features edge modes that persist over times scales well
in excess of the time needed for the bulk of the system to heat to infinite
temperatures.
