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arXiv · 2009.08425

Superuniversality of superdiffusion

Enej Ilievski·Jacopo De Nardis·Sarang Gopalakrishnan·Romain Vasseur·Brayden Ware
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Abstract

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 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 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 as 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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BibTeXRIS

Enej Ilievski, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware. 2020-09-17. Superuniversality of superdiffusion. https://doi.org/10.1103/physrevx.11.031023

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