Anomalous hydrodynamic fluctuations in the quantum XXZ spin chain
Abstract
The quantum XXZ spin-1/2 chain features non-Gaussian spin current fluctuations in the regime of easy-axis anisotropy. Using ballistic macroscopic fluctuation theory, we derive the exact probability distribution of typical spin-current fluctuations in thermal equilibrium. The obtained nested Gaussian distribution is fully characterized by its variance which we analytically relate to the spin diffusion constant and static spin susceptibility, and compare with numerical simulations. By unveiling how the same mechanism which leads to anomalous charge current fluctuations in single-file systems manifests itself in the XXZ chain, our approach establishes the universal hydrodynamic origin of the observed anomalous fluctuations.
Keywords
Cite
@article{arxiv.2602.24242,
title = {Anomalous hydrodynamic fluctuations in the quantum XXZ spin chain},
author = {Takato Yoshimura and Žiga Krajnik and Alvise Bastianello and Enej Ilievski},
journal= {arXiv preprint arXiv:2602.24242},
year = {2026}
}
Comments
v1:9+2 pages, 3 figures. v2: typos corrected and references added