Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

Sarang Gopalakrishnan, Romain Vasseur

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

Original languageEnglish (US)
Pages (from-to)159-176
Number of pages18
JournalAnnual Review of Condensed Matter Physics
StatePublished - Mar 11 2024
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Condensed Matter Physics


  • anomalous transport
  • hydrodynamics
  • quantum spin chains


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