  We explore the interspecies interaction quench dynamics of ultracold
spin-polarized few-body mass balanced Fermi-Fermi mixtures confined in a
double-well with an emphasis on the beyond Hartree-Fock correlation effects. It
is shown that the ground state of particle imbalanced mixtures exhibits a
symmetry breaking of the single-particle density for strong interactions in the
Hartree-Fock limit, which is altered within the many-body approach. Quenching
the interspecies repulsion towards the strongly interacting regime the two
species phase separate within the Hartree-Fock approximation while remaining
miscible in the many-body treatment. Despite their miscible character on the
one-body level the two species are found to be strongly correlated and exhibit
a phase separation on the two-body level that suggests the anti-ferromagnetic
like behavior of the few-body mixture. For particle balanced mixtures we show
that an intrawell fragmentation (filamentation) of the density occurs both for
the ground state as well as upon quenching from weak to strong interactions, a
result that is exclusively caused by the presence of strong correlations.
Inspecting the two-body correlations a phase separation of the two species is
unveiled being a precursor towards an anti-ferromagnetic state. Finally, we
simulate in-situ single-shot measurements and showcase how our findings can be
retrieved by averaging over a sample of single-shot images.
