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Abstract

We study the role of the anomalous E = 0 state in dynamical properties of noninteracting fermionic chains with chiral symmetry and correlated bond disorder in one dimension. These models possess 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.