Superuniversality of Superdiffusion

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

doi:10.1103/physrevx.11.031023

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=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.Received 24 October 2020Revised 4 May 2021Accepted 19 May 2021DOI:https://doi.org/10.1103/PhysRevX.11.031023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum statistical mechanicsQuantum transportTechniquesIntegrable systemsStatistical PhysicsGeneral Physics

Highlights

A complete characterization and classification of dynamical properties of isolated interacting many-body systems remains one of the central unsettled problems in statistical mechanics
For an integrable quantum model with local interactions, invariant under a global nonAbelian 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 1⁄4 3=2
Two prominent examples are integrable and many-body localized quantum systems [1,2,3], which feature extensively many conserved quantities and can persist in nonthermal “generalized Gibbs states” that are measurably different from the orthodox thermal ensemble [4,5,6,7,8,9]. Because these extensive conservation laws lead to nonstandard equilibrium states, and because hydrodynamics begins with an assumption of local thermal equilibrium, it follows that hydrodynamics is modified for integrable

Summary

Introduction

A complete characterization and classification of dynamical properties of isolated interacting many-body systems remains one of the central unsettled problems in statistical mechanics. Two prominent examples are integrable and many-body localized quantum systems [1,2,3], which feature extensively many conserved quantities and can persist in nonthermal “generalized Gibbs states” that are measurably different from the orthodox thermal ensemble [4,5,6,7,8,9]. Because these extensive conservation laws lead to nonstandard equilibrium states, and because hydrodynamics begins with an assumption of local thermal equilibrium, it follows that hydrodynamics is modified for integrable. Instead of normal diffusion, nondisordered integrable systems typically exhibit ballistic transport with finite Drude weights [10,11], whereas in localized models, transport is entirely absent [2]

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