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 , we find that finite-temperature transport of Noether charges associated with symmetry in thermal states that are invariant under is universally superdiffusive and characterized by the dynamical exponent . 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 2020
- Revised 4 May 2021
- Accepted 19 May 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031023
Published 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 Society
Physics Subject Headings (PhySH)
Popular Summary
Electrons in typical metals undergo diffusion: They bounce off impurities and collide with one another, so their motion resembles a random walk. When confined to one dimension, electrons can—under some conditions—move faster than diffusively. Here, entities called quasiparticles move ballistically, that is, without scattering backward. A more recently discovered phenomenon is “superdiffusive” transport, which is intermediate between ballistic motion and diffusion. In this work, we establish theoretically that a previously noted rate at which entities superdiffusively spread out holds across a wide range of systems.
In ballistic motion, the distance a particle travels scales linearly with time; for diffusion, the distance traveled scales as the square root of time. Superdiffusion occurs in a class of models known as “integrable.” Recently, some of these models were numerically seen to exhibit superdiffusion spreading that scaled as time to the power. Whether this exponent held across systems was unclear. Our work establishes that the exponent holds universally for integrable models with certain symmetries.
A key open question is how far superdiffusion persists in realistic experimental situations, where integrability is an approximate property. At short times, these imperfections should not matter and superdiffusion should persist; at long times, it presumably crosses over to regular diffusion, but the timescale for this crossover is an important unsolved problem.
