  We consider a quench in an infinite spin ladder describing a system with two
species of bosons in the limit of strong interactions. If the heavy bosonic
species has infinite mass the model becomes a spin chain with quenched binary
disorder which shows true Anderson localization (AL) or many-body localization
(MBL). For finite hopping amplitude $J'$ of the heavy particles, on the other
hand, we find an exponential polarization decay with a relaxation rate which
depends monotonically on $J'$. Furthermore, the entanglement entropy changes
from a constant (AL) or logarithmic (MBL) scaling in time $t$ for $J'=0$ to a
sub-ballistic power-law, $S_{\textrm{ent}}\sim t^\alpha$ with $\alpha< 1$, for
finite $J'$. We do not find a distinct regime in time where the dynamics for
$J'\neq 0$ shows the characteristics of an MBL phase. Instead, we discover a
time regime with distinct dephasing and entanglement times, different both from
a localized and a fully ergodic phase.
