A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Topological photonics emerged as a novel route to engineer the flow of light. Topologically
protected photonic edge modes, which are supported at the perimeters of topologically …

The bulk-boundary correspondence is among the central issues of non-Hermitian
topological states. We show that a previously overlooked “non-Hermitian skin effect” …

The relation between chiral edge modes and bulk Chern numbers of quantum Hall
insulators is a paradigmatic example of bulk-boundary correspondence. We show that the …

Capital to topological insulators, the bulk-boundary correspondence ties a topological
invariant computed from the bulk (extended) states with those at the boundary, which are …

Exceptional points (EPs) correspond to degeneracies of open systems. These are attracting
much interest in optics, optoelectronics, plasmonics, and condensed matter physics. In the …

Both theoretical and experimental studies of topological phases in non-Hermitian systems
have made a remarkable progress in the last few years of research. In this article, we review …

Recently, the search for topological states of matter has turned to non-Hermitian systems,
which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices …

We investigate the localization-delocalization transition in one-dimensional non-Hermitian
quasiperiodic lattices with exponential short-range hopping, which possess parity-time (PT) …

Recently, topological quantum states of non-Hermitian systems, exhibiting rich, new exotic
states, have attracted great attention in condensed-matter physics. As for the demonstration …