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Updated: Jul 10, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains
Jacopo De Nardis1, Sarang Gopalakrishnan2, Romain Vasseur3
1Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France.
Abstract:
Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.
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