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 …

For many years, the Luttinger liquid theory has served as a useful paradigm for the
description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is …

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 …

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 …

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

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 …

We address the nature of spin transport in the integrable XXZ spin chain, focusing on the
isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based …

We extend beyond the Euler scales the hydrodynamic theory for quantum and classical
integrable models developed in recent years, accounting for diffusive dynamics and local …

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems
when prepared in generic inhomogeneous initial states. However, the ballistic contribution …

An explicit matrix product ansatz is presented, in the first two orders in the (weak) coupling
parameter, for the nonequilibrium steady state of the homogeneous, nearest neighbor …