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Non-Hermiticity can destroy Anderson localization and lead to delocalizationeven in one dimension. However, the unified understanding of the non-Hermitiandelocalization has yet to be established. Here, we develop a scaling theory oflocalization in non-Hermitian systems. We reveal that non-Hermiticityintroduces a new scale and breaks down the one-parameter scaling, which is thecentral assumption of the conventional scaling theory of localization. Instead,we identify the origin of the unconventional non-Hermitian delocalization asthe two-parameter scaling. Furthermore, we establish the threefold universalityof non-Hermitian localization based on reciprocity; reciprocity forbids thedelocalization without internal degrees of freedom, whereas symplecticreciprocity results in a new type of symmetry-protected delocalization.

Nonunitary Scaling Theory of Non-Hermitian Localization