Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains

Jacopo De Nardis, Sarang Gopalakrishnan, Enej Ilievski, Romain Vasseur

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51 Scopus citations


Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles"that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.

Original languageEnglish (US)
Article number070601
JournalPhysical review letters
Issue number7
StatePublished - Aug 14 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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