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arXiv · 2502.04755

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

Jinghui Pi·Chenyang Wang·Yong-Chun Liu·Yangqian Yan
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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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Jinghui Pi, Chenyang Wang, Yong-Chun Liu, Yangqian Yan. 2025-02-07. Geometric origin of self-intersection points in non-Hermitian energy spectra. https://doi.org/10.1103/physrevb.111.165407

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