Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles" that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.
@article{arxiv.2003.13708,
title = {Superdiffusion from emergent classical solitons in quantum spin chains},
author = {Jacopo De Nardis and Sarang Gopalakrishnan and Enej Ilievski and Romain Vasseur},
journal= {arXiv preprint arXiv:2003.13708},
year = {2020}
}
Comments
Published version, updated Fig 2 and supplemental material