The XXZ spin chain is a canonical model of one-dimensional quantum magnetism. We consider spin transport at nonzero temperature in this model. Spin transport is ballistic in the easy-plane regime, diffusive in the easy-axis regime, and superdiffusive at the isotropic Heisenberg point. Energy transport, by contrast, is ballistic in all cases. The framework of generalized hydrodynamics offers an elementary explanation of these phenomena  in terms of the quasiparticle content of the XXZ model. It also predicts new transport anomalies, e.g., in local relaxation in the easy-axis regime in the presence of a magnetic field , and in the a.c. conductivity in the easy-plane regime . These anomalies come from the asymptotic behavior of large bound states of many quasiparticles, as we will discuss.
 SG, R. Vasseur, PRL 122, 127202 (2019)
 SG, R. Vasseur, B. Ware, PNAS 116, 16250 (2019)
 U. Agrawal, SG, R. Vasseur, and B. Ware, arXiv:1909.05263