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 …

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

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

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 …

Non-Hermiticity gives rise to unique topological phases that have no counterparts in
Hermitian systems. Such intrinsic non-Hermitian topological phases appear even in one …

Emergence of exceptional points in two dimensions is one of the remarkable phenomena in
non-Hermitian systems. We here elucidate the impacts of symmetry on the non-Hermitian …

We analyze a two-dimensional Kondo lattice model with special emphasis on non-Hermitian
properties of the single-particle spectrum, following a recent proposal by Kozii and Fu. Our …

We study a new class of non-Hermitian topological phases in three dimensions in the
absence of any symmetry, where the topological robust band degeneracies are Hopf-link …

We propose a novel type of skin effects in non-Hermitian quantum many-body systems that
we dub a “non-Hermitian Mott skin effect.” This phenomenon is induced by the interplay …

We investigate the entanglement dynamics of the non-Hermitian Aubry-André-Harper chain.
The results reveal that by increasing quasiperiodic strength, a phase transition occurs from …