Hydrodynamic Diffusion in Integrable Systems

Jacopo De Nardis, Denis Bernard, and Benjamin Doyon
Phys. Rev. Lett. 121, 160603 – Published 17 October 2018
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Abstract

We show that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models. We extend the recently developed generalized hydrodynamic (GHD) to include terms of Navier-Stokes type, which leads to positive entropy production and diffusive relaxation mechanisms. These terms provide the subleading diffusive corrections to Euler-scale GHD for the large-scale nonequilibrium dynamics of integrable systems, and arise due to two-body scatterings among quasiparticles. We give exact expressions for the diffusion coefficients. Our results apply to a large class of integrable models, including quantum and classical, Galilean and relativistic field theories, chains, and gases in one dimension, such as the Lieb-Liniger model describing cold atom gases and the Heisenberg quantum spin chain. We provide numerical evaluations in the Heisenberg XXZ spin chain, both for the spin diffusion constant, and for the diffusive effects during the melting of a small domain wall of spins, finding excellent agreement with time-dependent density matrix renormalization group numerical simulations.

  • Figure
  • Received 30 July 2018
  • Revised 21 September 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.160603

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Jacopo De Nardis1, Denis Bernard2, and Benjamin Doyon3

  • 1Département de Physique, Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
  • 2Laboratoire de Physique Théorique de l’Ecole Normale Supérieure de Paris, CNRS, ENS, PSL University & Sorbonne Université, 75005 Paris, France
  • 3Department of Mathematics, King’s College London, Strand WC2R 2LS London, United Kingdom

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Issue

Vol. 121, Iss. 16 — 19 October 2018

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