Nonunitary Scaling Theory of Non-Hermitian Localization

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

Automated summary

The authors developed a scaling theory of localization in non-Hermitian systems, revealing that non-Hermiticity introduces a new scale and breaks down the conventional one-parameter scaling theory of localization. The unconventional non-Hermitian delocalization is identified as originating from the two-parameter scaling. Furthermore, based on reciprocity, the authors established the threefold universality of non-Hermitian localization, where reciprocity prohibits delocalization without internal degrees of freedom, and symplectic reciprocity results in a new type of symmetry-protected delocalization.