Point-Gap Bound States in Non-Hermitian Systems

• URL: http://arxiv.org/abs/2305.11227v2
• Date: Fri, 23 Jun 2023 09:08:14 GMT
• Title: Point-Gap Bound States in Non-Hermitian Systems
• Authors: Zixi Fang, Chen Fang, and Kai Zhang
• Abstract summary: We investigate the impurity-induced bound states in 1D non-Hermitian systems. We establish an exact relationship between impurity potential and bound-state energy. We show that the bound states residing in the point gaps with nonzero spectral winding exhibit sensitivity to boundary conditions.
• Score: 15.127226844505927
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we systematically investigate the impurity-induced bound states in 1D non-Hermitian systems. By establishing an exact relationship between impurity potential and bound-state energy, we determine the minimum impurity potential required to generate bound states within each point energy gap. We demonstrate that the absence of Bloch saddle points necessitates a finite threshold of impurity potential; otherwise, infinitesimal impurity potential can create bound states. Furthermore, we show that the bound states residing in the point gaps with nonzero spectral winding exhibit sensitivity to boundary conditions and will be squeezed towards the edges when the boundaries are opened, indicating the bulk-boundary correspondence in terms of point-gap topology.

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