  We present a systematic study of spectral functions of a time-periodically
driven Falicov-Kimball Hamiltonian. In the high-frequency limit, this system
can be effectively described as a Harper-Hofstadter-Falicov-Kimball model.
Using real-space Floquet dynamical mean-field theory (DMFT), we take into
account interaction effects and contributions from higher Floquet bands in a
non-perturbative way. Our calculations show a high degree of similarity between
the interacting driven system and its effective static counterpart with respect
to spectral properties. However, as also illustrated by our results, one should
bear in mind that Floquet DMFT describes a non-equilibrium steady state (NESS),
while an effective static Hamiltonian describes an equilibrium state. We
further demonstrate the possibility of using real-space Floquet DMFT to study
edge states on a cylinder geometry.
