Diffusion in generalized hydrodynamics and quasiparticle scattering

De Nardis, Jacopo; Bernard, Denis; Doyon, Benjamin

doi:10.21468/SciPostPhys.6.4.049

SciPost Physics

Diffusion in generalized hydrodynamics and quasiparticle scattering

Jacopo De Nardis, Denis Bernard, Benjamin Doyon

SciPost Phys. 6, 049 (2019) · published 25 April 2019

doi: 10.21468/SciPostPhys.6.4.049
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.6.4.049
TI  - Diffusion in generalized hydrodynamics and quasiparticle scattering
PY  - 2019/04/25
UR  - https://scipost.org/SciPostPhys.6.4.049
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 6
IS  - 4
SP  - 049
A1  - De Nardis, Jacopo
AU  - Bernard, Denis
AU  - Doyon, Benjamin
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.6.4.049,
	title={{Diffusion in generalized hydrodynamics and quasiparticle scattering}},
	author={Jacopo De Nardis and Denis Bernard and Benjamin Doyon},
	journal={SciPost Phys.},
	volume={6},
	pages={049},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.6.4.049},
	url={https://scipost.org/10.21468/SciPostPhys.6.4.049},
}

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Ontology / Topics

See full Ontology or Topics database.

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

Authors / Affiliations: mappings to Contributors and Organizations

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Funders for the research work leading to this publication

Agence Nationale de la Recherche [ANR]
Erwin Schrödinger International Institute for Mathematics and Physics [ESI]
Gouvernement du Canada / Government of Canada
Ministry of Research and Innovation (Canada, Ontario, Min Res&Innov) (through Organization: Ministry of Research, Innovation and Science - Ontario [MRIS])
Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]
Thomas Young Centre / Thomas Young Centre [TYC]