Superuniversality of Superdiffusion

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

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46 Scopus citations


Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-Abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model with local interactions, invariant under a global non-Abelian simple Lie group , we find that finite-temperature transport of Noether charges associated with symmetry in thermal states that are invariant under is universally superdiffusive and characterized by the dynamical exponent . This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it “superuniversal.” The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations. We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters. We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua. Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

Original languageEnglish (US)
Article number031023
JournalPhysical Review X
Issue number3
StatePublished - Sep 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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