After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

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 …

Multipartite entangled states are crucial for numerous applications in quantum information
science. However, the generation and verification of multipartite entanglement on fully …

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

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 …

How do closed quantum many-body systems driven out of equilibrium eventually achieve
equilibration? And how do these systems thermalize, given that they comprise so many …

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum
matter constitutes a key challenge for current computational methods. This holds in …

A phase transition indicates a sudden change in the properties of a large system. For
temperature-driven phase transitions this is related to nonanalytic behavior of the free …