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 …

The many-body physics at quantum phase transitions shows a subtle interplay between
quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we …

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 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 …

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 …

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

We show that hydrodynamic diffusion is generically present in many-body, one-dimensional
interacting quantum and classical integrable models. We extend the recently developed …

These are lecture notes for a series of lectures given at the Les Houches Summer School on
Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same …

We review the imaginary time path integral approach to the quench dynamics of conformal
field theories. We show how this technique can be applied to the determination of the time …

We review recent progress in understanding the notion of locality in integrable quantum
lattice systems. The central concept concerns the so-called quasilocal conserved quantities …