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Physical Review X


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 G, we find that finite-temperature transport of Noether charges associated with symmetry G in thermal states that are invariant under G is universally superdiffusive and characterized by the dynamical exponent z = 3/2. 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.









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National Science Foundation under NSFNational Science Foundation (NSF) [DMR-1653271]; US Department of Energy, Office of Science, Basic Energy Sciences, under Early Career AwardUnited States Department of Energy (DOE) [DE-SC0019168]; Alfred P. Sloan Foundation through a Sloan Research FellowshipAlfred P. Sloan Foundation; Research Foundation FlandersFWO; Slovenian Research Agency (ARRS) programSlovenian Research Agency - Slovenia [P1-0402]

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