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 …

Many experimentally relevant quantum spin chains are approximately integrable, and
support long-lived quasiparticle excitations. A canonical example of integrable model of …

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of
a wealth of classical stochastic models. Surprisingly, KPZ universality was recently …

Simple models of interacting spins have an important role in physics. They capture the
properties of many magnetic materials, but also extend to other systems, such as bosons …

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 …

Equilibrium spatiotemporal correlation functions are central to understanding weak
nonequilibrium physics. In certain local one-dimensional classical systems with three …

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 …

Classical hydrodynamics is a remarkably versatile description of the coarse-grained
behaviour of many-particle systems once local equilibrium has been established. The form …

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 …