Anderson transition in disordered Hatano-Nelson systems

TL;DR

This paper investigates the transition mechanism between the non-Hermitian skin effect and Anderson localization in disordered Hatano-Nelson systems, linking topological invariants to localization phenomena through Lyapunov exponents.

Contribution

It provides a universal criterion connecting topological invariant changes to eigenvector crossover, advancing understanding of localization transitions in non-Hermitian systems.

Findings

Established a proof linking topological invariant change to eigenvector crossover.

Identified Lyapunov exponents as key to understanding the transition.

Unified the description of skin effect and Anderson localization in disordered systems.

Abstract

We illuminate the fundamental mechanism responsible for the transition between the non-Hermitian skin effect and defect-induced Anderson localization in the bulk via the study of Lyapunov exponents. We obtain a proof that the change of the topological invariant associated with an eigenvalue coincides with the eigenvector crossover from non-Hermitian skin effect to Anderson localization, establishing a universal criterion for localization behavior.