Speaker
Description
The unidirectional Hatano-Nelson chain serves as the fundamental non-Hermitian building block of the Su-Schrieffer-Heeger (SSH) model. We investigate its Anderson localization properties under diagonal binary disorder. For weak disorder, the complex eigenvalue spectrum forms a single closed loop, which bifurcates into two distinct loops at a critical disorder threshold. Correspondingly, the spectral winding number undergoes a transition from 1 in the weak-disorder regime, through 1/2 at the critical point, to 0 in the strong-disorder limit. We show that the eigenstates are subexponentially localized, with a localization length that varies analytically as a function of the loop parameter. Notably, at weak and critical disorder, the spectrum hosts two completely delocalized states with diverging localization lengths. These findings remain robust under various boundary conditions, with the exception of strictly open boundaries. We also discuss to more complicated disorder, relate these findings to generalized Cassini ovals, and generalize to arbitrary lattice dimensions and Hermitian or non-Hermitian models with correlated hopping and onsite disorder.