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Diffusion in generalized hydrodynamics and quasiparticle scattering

by Jacopo De Nardis, Denis Bernard, Benjamin Doyon

Submission summary

As Contributors: Jacopo De Nardis · Benjamin Doyon
Arxiv Link: https://arxiv.org/abs/1812.00767v4
Date accepted: 2019-04-15
Date submitted: 2019-04-04
Submitted by: De Nardis, Jacopo
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Condensed Matter Physics - Theory

Abstract

We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reached via a gradient expansion of the expectation values of the conserved fields and how the coefficients of the expansion can be computed via integrated steady-state two-point correlation functions, emphasising that PT-symmetry can fully fix the inherent ambiguity in the definition of conserved fields at the diffusive scale. We develop a form factor expansion to compute such correlation functions and we show that, while the dynamics at the Euler scale is completely determined by the density of single quasiparticle excitations on top of the local steady state, diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems. We then show that only two-quasiparticle scattering processes contribute to the diffusive dynamics. Finally we employ the theory to compute the exact spin diffusion constant of a gapped XXZ spin-1/2 chain at finite temperature and half-filling, where we show that spin transport is purely diffusive.

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Ontology / Topics

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Correlation functions Euler hydrodynamics Generalized hydrodynamics (GHD) Quantum spin chains Quasiparticles XXZ model

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Comments

Anonymous on 2019-04-09

This is very interesting work with an extensive bibliography. I think it would have been interesting to include in the bibliography the classic work of Kadanoff and Martin on hydrodynamic equations and correlation functions, Annals of Physics, 24, 419 (1963).