Topological enhancement of non-normality in non-Hermitian skin effects

• URL: http://arxiv.org/abs/2304.06689v3
• Date: Tue, 13 Feb 2024 14:11:59 GMT
• Title: Topological enhancement of non-normality in non-Hermitian skin effects
• Authors: Yusuke O. Nakai, Nobuyuki Okuma, Daichi Nakamura, Kenji Shimomura, Masatoshi Sato
• Abstract summary: The non-Hermitian skin effects are representative intrinsic phenomena to non-Hermitian systems. This paper reveals that topological enhancement of non-normality under the open boundary condition accurately quantifies the non-Hermitian skin effects.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.

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