  Using exact diagonalization methods we study possible phases in a one
dimensional model of two differently populated fermionic species in a
periodically driven optical lattice. The shaking amplitude and frequency are
chosen to resonantly drive $s-p$ transition while minimizing the standard
intraband tunnelings. We numerically verify that in the vicinity of vanishing
intraband tunnelings the system, for an appropriate filling, shows an emergent
density wave configuration of composites. The majority fermions moving in such
a lattice mimic the celebrated Rice-Mele model. Far away from that region
structure changes to clustered phase, with intermediate phase abundantly
populated by defects of the density wave. These defects lead to loclaized modes
carrying fractional particle charge. The results obtained are compared with
earlier mean field approximation predictions.
