Superuniversality of superdiffusion

TL;DR

This paper demonstrates that in integrable quantum models with non-abelian symmetry, finite-temperature transport of Noether charges is universally superdiffusive with a dynamical exponent of 3/2, regardless of microscopic details.

Contribution

It provides a group-theoretic framework explaining superdiffusive transport in integrable models with non-abelian symmetry, establishing superuniversality across different systems.

Findings

Finite-temperature transport of Noether charges is superdiffusive with z=3/2.

Superdiffusion is independent of microscopic details and symmetry specifics.

Giant quasiparticles are identified as nonlinear soliton modes in classical field theories.

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.