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 sparked great interest in fundamental physics and inspired a wide range 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 high-dimensional eigenspaces and overlapped spectra. This condition is denoted as “exceptional deficiency.” When this happens, two eigenspaces 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 is a route to go beyond the bulk-edge correspondence of non-Hermitian skin effects, which relates nontrivial point-gap topology to the existence of skin modes.
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
Prof Guancong Ma
Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China