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Hydrodynamic Diffusion in Integrable Systems.

Jacopo De Nardis1, Denis Bernard2, Benjamin Doyon3

  • 1Département de Physique, Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France.

Physical Review Letters
|November 3, 2018
PubMed
Summary
This summary is machine-generated.

Hydrodynamic diffusion is a common feature in one-dimensional quantum and classical integrable systems. This study extends generalized hydrodynamics to include Navier-Stokes terms, explaining diffusive relaxation and providing exact diffusion coefficients.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Dynamics

Background:

  • Integrable models in one dimension exhibit unique nonequilibrium dynamics.
  • Generalized hydrodynamics (GHD) describes Euler-scale dynamics but often lacks diffusive effects.
  • Understanding diffusive transport is crucial for describing realistic many-body systems.

Purpose of the Study:

  • To demonstrate the generic presence of hydrodynamic diffusion in 1D interacting quantum and classical integrable models.
  • To extend GHD by incorporating Navier-Stokes-type terms for diffusive relaxation.
  • To derive exact expressions for diffusion coefficients and validate them numerically.

Main Methods:

  • Extension of generalized hydrodynamics (GHD) to include Navier-Stokes terms.
  • Derivation of exact analytical expressions for diffusion coefficients.
  • Numerical simulations using the Heisenberg XXZ spin chain and comparison with time-dependent density matrix renormalization group (tDMRG) methods.

Main Results:

  • Hydrodynamic diffusion is shown to be a generic phenomenon in 1D integrable systems.
  • The extended GHD framework predicts positive entropy production and diffusive relaxation.
  • Exact diffusion coefficients are derived and show excellent agreement with tDMRG simulations for spin diffusion and domain wall melting.

Conclusions:

  • The inclusion of Navier-Stokes terms in GHD captures essential diffusive corrections to Euler-scale dynamics.
  • The findings are broadly applicable to various 1D quantum and classical integrable models.
  • This work provides a robust theoretical framework and numerical validation for hydrodynamic diffusion in integrable systems.