Superdiffusion in spin chains

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.

Automated summary

This review summarizes recent advances in understanding anomalous transport in spin chains, particularly through the lens of integrability. Numerical methods based on tensor-network techniques have revealed anomalous transport in many canonical integrable spin chains, such as the Heisenberg model. The framework of generalized hydrodynamics has been extended to explain some of the underlying mechanisms of anomalous transport, with discussions on similarities and differences with other contexts. Further, potential transport anomalies in systems with emergent or approximate integrability are briefly reviewed, with ongoing research on anomalous transport and dynamics.