Geometric origin of self-intersection points in non-Hermitian energy spectra

• URL: http://arxiv.org/abs/2502.04755v2
• Date: Wed, 09 Apr 2025 18:32:28 GMT
• Title: Geometric origin of self-intersection points in non-Hermitian energy spectra
• Authors: Jinghui Pi, Chenyang Wang, Yong-Chun Liu, Yangqian Yan,
• Abstract summary: Unlike Hermitian systems, non-Hermitian energy spectra can form closed loops in the complex energy plane.<n>We rigorously demonstrate that these self-intersection points result from the intersection of the auxiliary generalized Brillouin zone and the Brillouin zone in one-band systems.
• Score: 1.985724084078542
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Unlike Hermitian systems, non-Hermitian energy spectra under periodic boundary conditions can form closed loops in the complex energy plane, a phenomenon known as point gap topology. In this paper, we investigate the self-intersection points of such non-Hermitian energy spectra and reveal their geometric origins. We rigorously demonstrate that these self-intersection points result from the intersection of the auxiliary generalized Brillouin zone and the Brillouin zone in one-band systems, as confirmed by an extended Hatano-Nelson model. This finding is further generalized to multi-band systems, illustrated through a non-Hermitian Su-Schrieffer-Heeger model. Moreover, we address multiple self-intersection points and derive the geometric conditions for general n-fold self-intersection points. Our results enhance the fundamental understanding of generic non-Hermitian quantum systems and provide theoretical support for further experimental investigations of energy self-intersection points.

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