This review gives a pedagogical introduction to the eigenstate thermalization hypothesis
(ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first …

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a
proxy for thermalization, has recently been proposed and studied in the context of symmetry …

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ
spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state …

The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe
observables in isolated integrable quantum systems after equilibration. Since then, the GGE …

We review the dynamics after quantum quenches in integrable quantum spin chains. We
give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the …

Entanglement and entropy are key concepts standing at the foundations of quantum and
statistical mechanics. Recently, the study of quantum quenches revealed that these …

This review is devoted to the problem of thermalization in a small isolated conglomerate of
interacting constituents. A variety of physically important systems of intensive current interest …

We address the hydrodynamics of operator spreading in interacting integrable lattice
models. In these models, operators spread through the ballistic propagation of …

In integrable many-particle systems, it is widely believed that the stationary state reached at
late times after a quantum quench can be described by a generalized Gibbs ensemble …