Robustness of algebraic localization under non-Hermitian extensions and skin effects

Determine whether the algebraically localized phases of the one-dimensional disordered long-range correlated hopping model with power-law hopping j_{n−m}∝e^{iθ sign(n−m)}/|n−m|^a persist when asymmetric non-Hermitian hopping is introduced (generalizing the Hatano–Nelson model to long-range correlated systems). In particular, establish if and how non-Hermitian spectral flow and the non-Hermitian skin effect affect the existence and properties of these algebraically localized phases.

Background

The study focuses on a Hermitian Hamiltonian with complex hopping phases that break time-reversal symmetry but preserve Hermiticity, and shows algebraic localization robust up to a critical phase. Extending to non-Hermitian asymmetric hopping would connect to the Hatano–Nelson physics in systems with long-range correlated hopping.

The authors highlight uncertainty regarding whether algebraically localized phases survive under non-Hermitian spectral flow and potential skin effects, motivating a systematic analysis of localization and transport in the non-Hermitian generalization.