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arXiv · 2107.03705

Scaling rule in critical non-Hermitian skin effect

Kazuki Yokomizo·Shuichi Murakami
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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.

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Kazuki Yokomizo, Shuichi Murakami. 2021-10-11. Scaling rule in critical non-Hermitian skin effect. https://doi.org/10.1103/physrevb.104.165117

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