Anomalous hydrodynamic fluctuations in the quantum XXZ spin chain

TL;DR

This paper derives the exact probability distribution of spin-current fluctuations in the quantum XXZ spin chain, revealing universal hydrodynamic mechanisms behind anomalous fluctuations in quantum many-body systems.

Contribution

It introduces a ballistic macroscopic fluctuation theory approach to analytically characterize non-Gaussian spin current fluctuations in the XXZ chain.

Findings

Exact nested Gaussian distribution for spin-current fluctuations

Analytical relation between variance, spin diffusion, and susceptibility

Numerical simulations confirming theoretical predictions

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.