  Ultracold fermions in a one-dimensional, spin-dependent, optical lattice are
described by a non-standard Hubbard model with next-nearest-neighbour
correlated hopping. Periodic driving of the lattice allows wide tuning of the
system parameters. We solve this model exactly for a special value of the
correlated hopping. The solution reveals the general properties of this system
for arbitrary filling: exact and asymmetric spin-charge separation, a gapless
spectrum of lowest energy excitations, a spin-gap, which may be interpreted in
terms of collective hole pairing and a non-vanishing den Nijs-Rommelse type
string correlator. Numerical studies away from the integrable point show the
persistence of both long range string order and spin-gap.
