Anomalous transport from hot quasiparticles in interacting spin chains

Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

Automated summary

This article reviews the transport properties of the XXZ spin chain using a intuitive quasiparticle picture based on the framework of generalized hydrodynamics. It discusses the emergence of anomalous linear response properties from hierarchies of quasiparticles in both integrable and near-integrable limits, with a focus on the role of hydrodynamic fluctuations. The article also comments on recent developments including non-linear response, full-counting statistics, and far-from-equilibrium transport, and provides an overview of recent numerical and experimental results on transport in XXZ spin chains.