Work

Superuniversality of Superdiffusion

Year: 2021

Type: article

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 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 ¼ 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.

Source: Physical Review X

DOI: 10.1103/physrevx.11.031023

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