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 current understanding of the role of topology in non-Hermitian (NH) systems and its far-
reaching physical consequences observable in a range of dissipative settings are reviewed …

Recent years have seen remarkable development in open quantum systems effectively
described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological …

We study the Hatano-Nelson model, ie, a one-dimensional non-Hermitian chain of spinless
fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest …

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 …

In this Letter, we study the conditions under which on-site dissipations can induce non-
Hermitian skin modes in non-Hermitian systems. When the original Hermitian Hamiltonian …

We revisit the fate of the skin modes in many-body non-Hermitian fermionic systems.
Contrary to the single-particle case, the many-body ground state cannot exhibit an …

The Aubry-André-Harper (AAH) model with a self-dual symmetry plays an important role in
studying the Anderson localization. Here we find a self-dual symmetry determining the …

The explorations of non-Hermiticity have been devoted to investigate the disorder-induced
many-body localization (MBL). However, the sensitivity of the spatial boundary conditions …

Non-Hermitian quantum many-body systems are a fascinating subject to be explored. Using
the generalized density matrix renormalization group method and complementary exact …