Superdiffusion in spin chains

TL;DR

This review discusses recent progress in understanding anomalous transport in integrable spin chains, highlighting numerical and theoretical advances, especially in generalized hydrodynamics, and identifying open questions in the field.

Contribution

It synthesizes recent developments in tensor-network simulations and generalized hydrodynamics to explain anomalous transport mechanisms in integrable spin chains.

Findings

Transport in many integrable spin chains is anomalous.

Generalized hydrodynamics explains some mechanisms of anomalous transport.

Potential anomalies in systems with emergent or approximate integrability.

Abstract

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-network methods, have shown that transport in many canonical integrable spin chains -- most famously the Heisenberg model -- is anomalous. Concurrently, the framework of generalized hydrodynamics has been extended to explain some of the mechanisms underlying anomalous transport. We present what is currently understood about these mechanisms, and discuss how they resemble (and differ from) the mechanisms for anomalous transport in other contexts. We also briefly review potential transport anomalies in systems where integrability is an emergent or approximate property. We survey instances of anomalous transport and dynamics that remain to be understood.