Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains

TL;DR

This paper develops a non-linear fluctuating hydrodynamic theory for isotropic spin chains, explaining superdiffusive spin transport with KPZ scaling and symmetric fluctuation distributions, supported by numerical simulations.

Contribution

It introduces a coupled stochastic mode theory that accounts for anomalous spin dynamics and deviations from standard KPZ predictions in isotropic spin chains.

Findings

Predicts KPZ scaling for spin structure factor

Shows symmetric, quasi-Gaussian spin fluctuation distribution

Supports theory with matrix-product states calculations

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/stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a non-linear 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.