  We study the effects of a periodically driven electric field applied to a
variety of tight-binding models in one dimension. We first consider a
non-interacting system with or without a staggered on-site potential, and we
find that that periodic driving can generate states localized completely or
partially near the ends of a finite-sized system. Depending on the system
parameters, such states have Floquet eigenvalues lying either outside or inside
the continuum of eigenvalues of the bulk states; only in the former case we
find that these states are completely localized at the ends and are true edge
states. We then consider a system of two bosonic particles which have an
on-site Hubbard interaction and show that a periodically driven electric field
can generate two-particle states which are localized at the ends of the system.
We show that many of these effects can be understood using a Floquet
perturbation theory which is valid in the limit of large staggered potential or
large interaction strength. Some of these effects can also be understood
qualitatively by considering time-independent Hamiltonians which have a
potential at the sites at the edges; Hamiltonians of these kind effectively
appear in a Floquet-Magnus analysis of the driven problem. Finally, we discuss
how the edge states produced by periodic driving of a non-interacting system of
fermions can be detected by measuring the differential conductance of the
system.
