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 …

Over the last decade impressive progress has been made in the theoretical understanding
of transport properties of clean, one-dimensional quantum lattice systems. Many physically …

We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and
Floquet quantum systems using the language of commutant algebras, the algebra of all …

Understanding the general principles underlying strongly interacting quantum states out of
equilibrium is one of the most important tasks of current theoretical physics. With …

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 …

Recent years have seen tremendous progress in the theoretical understanding of quantum
systems driven dissipatively by coupling to different baths at their edges. This was possible …

This review summarizes recent advances in our understanding of anomalous transport in
spin chains, viewed through the lens of integrability. Numerical advances, based on tensor …

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 …

The study of open quantum systems often relies on approximate master equations derived
under the assumptions of weak coupling to the environment. However when the system is …

We give a pedagogical introduction to the generalized hydrodynamic approach to
inhomogeneous quenches in integrable many-body quantum systems. We review recent …