  Motivated by recent experiments in fermionic polar gases, we study the
non-equilibrium dynamics of two-component dipolar fermions subject to a
quasiperiodic potential. We investigate the localization of charge and spin
degrees of freedom time evolving with a long-range spin-SU(2) symmetric
fermionic Hamiltonian, by calculating experimentally accessible dynamical
observables. To study the non-equilibrium dynamics, we start the time evolution
with two initial states at half-filling: (i) product state with doublons
$|\uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow
\downarrow 0 \uparrow \downarrow \rangle$ and (ii) product state with singlons
$|\uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \
\uparrow \ \downarrow \ \uparrow \ \downarrow \ \rangle$. We carried out the
real-time evolution via the fermionic Hamiltonian using exact
diagonalization(ED) and the time-dependent variational principle (TDVP) for
finite Matrix product states(MPSs), within experimentally relevant time scales.
For the product state with doublons, we observe a delocalized to localized
phase transition varying disorder strengths, by monitoring the decay of charge
imbalance with time. For the long-range interacting Hamiltonian of our focus,
and in the presence of strong enough disorder, starting the time evolution with
singlons we find a strong reduction in the spin delocalization, contrary to
results of previous studies using the disordered short-range (on-site) Hubbard
model with SU(2) symmetry. Our predictions for localization of both charge and
spin should be observable in ultra-cold experiments with fermionic dipolar
atoms subject to a quasiperiodic potential.
