  We discuss nonergodic dynamics of interacting spinless fermions in a tilted
optical lattice as modeled by XXZ spin chain in magnetic (or electric) field
changing linearly across the chain. The time dynamics is studied using exact
propagation for small chains and matrix product states techniques for larger
system sizes. We consider both the initial N\'eel separable state as well as
the quantum quench scenario in which the initial state may be significantly
entangled. We show that the entanglement dynamics is significantly different in
both cases. In the former a rapid initial growth is followed by a saturation
for sufficiently large tilt, $F$. In the latter case the dynamics seems to be
dominated by pair tunneling and the effective tunneling rate scales as $1/F^2$.
In the presence of an additional harmonic potential the imbalance is found to
be entirely determined by a local effective tilt, $F_{\text{loc}}$, the
entanglement entropy growth is modulated with frequency that follows
$1/F_{loc}^2$ scaling first but at long time the dynamics is determined rather
by the curvature of the harmonic potential. Only for large tilts or
sufficiently large curvatures, corresponding to the deeply localized regime, we
find the logarithmic entanglement growth for N\'eel initial state. The same
curvature determines long-time imbalance for large $F$ which reveals strong
revival phenomena associated with the manifold of equally spaced states,
degenerate in the absence of the harmonic potential.
