Scaling rule in critical non-Hermitian skin effect

Abstract

Non-Hermitian systems show a non-Hermitian skin effect, where the bulk states are localized at a boundary of the systems with open boundary conditions. In this paper, we study dependence of the localization length of the eigenstates on a system size in a specific non-Hermitian model with a critical non-Hermitian skin effect, where the energy spectrum undergoes discontinuous transition in the thermodynamic limit. We analytically show that the eigenstates exhibit remarkable localization, known as scale-free localization, where the localization length is proportional to a system size. Our result gives a theoretical support for the scale-free localization, which has been proposed only numerically in previous works.

arXiv comment8 pages, 4 figures

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• Non-Hermitian skin effect and self-acceleration
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Bloch bands in two-dimensional non-Hermitian systems
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• A non-Hermitian optical atomic mirror
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• Observation of non-local impedance response in a passive electrical circuit
• Non-Hermitian physics of levitated nanoparticle array