Absence of Normal Fluctuations in an Integrable Magnet

TL;DR

This paper studies the fluctuation behavior of magnetization in an integrable spin chain, revealing normal fluctuations in ballistic regimes and anomalous, divergent fluctuations in diffusive regimes, linked to soliton modes.

Contribution

It uncovers the dependence of fluctuation structures on dynamical scales and shows that anomalous fluctuations are tied to integrability and soliton presence.

Findings

Normal fluctuations in ballistic regime with finite cumulants.

Divergent scaled cumulants in diffusive and superdiffusive regimes.

Anomalous fluctuation features disappear when integrability is broken.

Abstract

We investigate dynamical fluctuations of transferred magnetization in the one-dimensional lattice Landau--Lifshitz magnet with uniaxial anisotropy, representing an emblematic model of interacting spins. We demonstrate that the structure of fluctuations in thermal equilibrium depends radically on the characteristic dynamical scale. In the ballistic regime, typical fluctuations are found to follow a normal distribution and scaled cumulants are finite. In stark contrast, on the diffusive and superdiffusive timescales, relevant respectively for the easy-axis and isotropic magnet at vanishing total magnetization, typical fluctuations are no longer Gaussian and, remarkably, scaled cumulants are divergent. The observed anomalous features disappear upon breaking integrability, suggesting that the absence of normal fluctuations is intimately tied to the presence of soliton modes. In a nonequilibrium setting of the isotropic magnet with weakly polarized step-profile initial state we find a slow drift of dynamical exponent from the superdiffusive towards the diffusive value.