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

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.

5 pages, 4 figures + appendix, version published in Phys. Rev. B

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• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Electronic Transport in DNA
• Quantum criticality of hot random spin chains
• Enhancement of localization in one-dimensional random potentials with long-range correlations

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• Band-center metal-insulator transition in bond-disordered graphene
• Effects of critical correlations on quantum percolation in two dimensions
• Floquet dynamics of disordered bands with isolated critical energies