Hydrodynamic Diffusion in Integrable Systems

TL;DR

This paper extends generalized hydrodynamics to include diffusive effects in integrable systems, providing exact diffusion coefficients and demonstrating their relevance across various models through numerical validation.

Contribution

It introduces Navier-Stokes type diffusive terms into GHD for integrable models, offering exact formulas for diffusion coefficients and broad applicability.

Findings

Diffusive corrections are present in many integrable models.

Exact expressions for diffusion coefficients are derived.

Numerical results agree with tDMRG simulations.

Abstract

We show that hydrodynamic diffusion is generically present in many-body interacting integrable models. We extend the recently developed generalised hydrodynamic (GHD) to include terms of Navier-Stokes type which lead to positive entropy production and diffusive relaxation mechanisms. These terms provide the subleading diffusive corrections to Euler-scale GHD for the large-scale non-equilibrium 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 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 tDMRG numerical simulations.