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Generalization of exceptional points: high-dimensional coalescing non-Hermitian spaces

Guancong Ma (Hong Kong Baptist University, Kowloon Tong, Hong Kong, China)

Abstract: Exceptional points (EPs) are spectral singularities in non-Hermitian systems, at which individual eigenvalues and eigenvectors become identical. The successful realization of EPs in diverse physical systems, such as photonics, acoustics, cold atoms, and superconducting circuits, has triggered tremendous interest in fundamental physics and inspired a vast array of novel applications. However, as the term “exceptional” suggests, EPs are usually isolated spectral points. Consequently, functionalities rooted in EPs face several inherent limitations, such as narrow bandwidth. Here, we present a generalization of the concept of EPs characterized by the coalescence of multi-dimensional Hilbert subspaces and overlapped spectra. This condition is denoted as “exceptional deficiency.” When this happens, two Hilbert subspaces of identical but arbitrarily large dimensions exactly align, accompanied by the coincidence of their spectra. Consequently, the full Hilbert space is highly defective by “missing” half of its span. In the meantime, the spectrum is entirely composed of EPs.

The condition of exceptional deficiency can be reached in a large variety of systems. We present its realization in a one-dimensional double-chain lattice. Intriguingly, the exceptional deficiency can break the bulk-edge correspondence of non-Hermitian skin effects, which relates nontrivial point-gap topology to the existence of skin modes. As a consequence, we find that the exceptional deficiency underpins new non-Hermitian phenomena characterized by the synergy of skin effects and propagation.

Reference

Zhen Li, Xulong Wang, Rundong Cai, Kenji Shimomura, Congwei Lu, Zhesen Yang, Masatoshi Sato, Guancong Ma, “Exceptional deficiency of non-Hermitian systems,” Nature Physics (2026). DOI: 10.1038/s41567-026-03259-7