  We study the role of the anomalous $E=0$ state in dynamical properties of
non-interacting fermionic chains with chiral symmetry and correlated bond
disorder in one dimension. These models posses a diverging density of states at
zero energy leading to a divergent localization length at the band center. By
analytically calculating the localization length for a finite system, we show
that correlations in the disorder modify the spatial decay of the $E = 0$ state
from being quasilocalized to extended. We numerically simulate charge and
entanglement propagation and provide evidence that states close to $E=0$
dominate the dynamical properties. Remarkably, we find that correlations lead
to subdiffusive charge propagation, whereas the growth of entanglement is
logarithmically slow. A logarithmic scaling of entanglement saturation with
system size is also observed, which indicates a behavior akin to quantum
critical glasses.
