Superdiffusion in spin chains

Vir B. Bulchandani, Sarang Gopalakrishnan, Enej Ilievski

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


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.

Original languageEnglish (US)
Article number084001
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number8
StatePublished - Aug 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Quantum transport in one-dimension


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