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 …

We review the methodology to theoretically treat parity-time-(PT-) symmetric, non-Hermitian
quantum many-body systems. They are realized as open quantum systems with PT …

Non-Hermitian quantum many-body systems are attracting widespread interest for their
exotic properties, including unconventional quantum criticality and topology. Here, we study …

The bulk states of Hermitian systems are believed insensitive to local Hermitian impurities or
perturbations except for a few impurity-induced bound states. Thus, it is important to ask …

Surpassing the individual characteristics of the non-Hermitian skin effect (NHSE) and the
scale-free (SF) effect observed recently, we systematically exploit the exponential decay …

By utilizing biorthogonal bases, we develop a comprehensive framework for studying
biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help …

We present a systematic study of statistical mechanics for non-Hermitian quantum systems.
Our work reveals that the stability of a non-Hermitian system necessitates the existence of a …

We develop a diagrammatic Monte Carlo method for the real-time dynamics of dissipative
quantum impurity models. These are small open quantum systems with interaction and local …

We generalize the vertex expansion approach of the functional renormalization group to non-
Hermitian systems. As certain anomalous expectation values might not vanish, additional …

We use a noisy signal with finite correlation time to drive a spin (dissipative impurity) in the
quantum XY spin chain and calculate the dynamics of entanglement entropy (EE) of a …