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 nontrivial 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 nonnormality under the OBC accurately quantifies the non-Hermitian skin effects. Corresponding to spectrum and state changes of the skin effects, we introduce two scalar measures of nonnormality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced nonnormality 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 nonnormality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.
10 More- Received 1 May 2023
- Accepted 5 April 2024
DOI:https://doi.org/10.1103/PhysRevB.109.144203
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