Non-Hermitian delocalization in 1D via emergent compactness

TL;DR

This paper reveals a novel delocalization mechanism in 1D non-Hermitian systems with imaginary disorder, where specific structured disorder induces an infinite localization length, contrasting with typical Anderson localization.

Contribution

It introduces a new route to delocalization in 1D non-Hermitian systems via structured imaginary potential disorder that creates an SU(2) transfer matrix with infinite localization length.

Findings

Structured imaginary disorder can induce delocalization in 1D systems.

The SU(2) transfer matrix structure is key to infinite localization length.

Boundary conditions can tune the fraction of delocalized states.

Abstract

Potential disorder in 1D leads to Anderson localization of the entire spectrum. Upon sacrificing hermiticity by adding non-reciprocal hopping, the non-Hermitian skin effect competes with localization. We find another route for delocalization, which involves imaginary potential disorder. While an entirely random potential generally still leads to localization, imposing minimal spatial structure to the disorder can protect delocalization: it endows the concomitant transfer matrix with an SU(2) structure, whose compactness in turn translates into an infinite localization length. The fraction of delocalized states can be tuned by the choice of boundary conditions.