Generalized Dyson model: nature of zero mode and its implication in dynamics

TL;DR

This paper investigates how correlated disorder affects the zero-energy state in one-dimensional chiral symmetric fermionic chains, revealing extended states, subdiffusive charge transport, and slow entanglement growth indicative of quantum criticality.

Contribution

It analytically and numerically demonstrates the impact of disorder correlations on zero-energy states and their influence on dynamics, highlighting a transition from localized to extended states and critical behavior.

Findings

Correlations modify zero-energy state from localized to extended.

Charge propagation becomes subdiffusive due to correlations.

Entanglement growth is logarithmically slow, indicating critical behavior.

Abstract

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.