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

Yusuke O. Nakai; Nobuyuki Okuma; Daichi Nakamura; Kenji Shimomura; Masatoshi Sato

doi:10.1103/physrevb.109.144203

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arXiv · 2304.06689

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

Yusuke O. Nakai·Nobuyuki Okuma·Daichi Nakamura·Kenji Shimomura·Masatoshi Sato

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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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Yusuke O. Nakai, Nobuyuki Okuma, Daichi Nakamura, Kenji Shimomura, Masatoshi Sato. 2023-04-13. Topological enhancement of non-normality in non-Hermitian skin effects. https://doi.org/10.1103/physrevb.109.144203

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