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 …

Quantum impurity models describe an atom or molecule embedded in a host material with
which it can exchange electrons. They are basic to nanoscience as representations of …

The study of nonequilibrium phenomena in correlated lattice systems has developed into
one of the most active and exciting branches of condensed matter physics. This research …

We introduce an efficient method to simulate the dynamics of an interacting quantum
impurity coupled to noninteracting fermionic reservoirs. Viewing the impurity as an open …

We solve the impurity problem which arises within nonequilibrium dynamical mean-field
theory for the Hubbard model by means of a self-consistent perturbation expansion around …

Recently, dynamical phase transitions have been identified based on the nonanalytic
behavior of the Loschmidt echo in the thermodynamic limit [Heyl et al., Phys. Rev. Lett. 110 …

We develop an iterative, numerically exact approach for the treatment of nonequilibrium
quantum transport and dissipation problems that avoids the real-time sign problem …

Accurate characterization of correlated electronic states, as well as their evolution under
external fields or in dissipative environment, is essentially important for understanding the …

We present an infinite Grassmann time-evolving matrix product operator method for
quantum impurity problems, which directly works in the steady state. The method embraces …

We present a brief pedagogical review of theoretical Green's function methods applicable to
open quantum systems out of equilibrium, in general, and single molecule junctions, in …