Nonunitary Scaling Theory of Non-Hermitian Localization

• URL: http://arxiv.org/abs/2005.00604v2
• Date: Thu, 22 Apr 2021 20:53:51 GMT
• Title: Nonunitary Scaling Theory of Non-Hermitian Localization
• Authors: Kohei Kawabata, Shinsei Ryu
• Abstract summary: We develop a scaling theory of localization in non-Hermitian systems. We establish the threefold universality of non-Hermitian localization based on reciprocity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermiticity can destroy Anderson localization and lead to delocalization even in one dimension. However, the unified understanding of the 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 the unconventional non-Hermitian delocalization as the two-parameter scaling. Furthermore, we establish the threefold universality of non-Hermitian localization based on reciprocity; reciprocity forbids the delocalization without internal degrees of freedom, whereas symplectic reciprocity results in a new type of symmetry-protected delocalization.

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