Anomalous Hydrodynamic Fluctuations in the Quantum XXZ Spin Chain.

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 asymptotic probability distribution of typical spin-current fluctuations in thermal equilibrium at zero average magnetization. The obtained nested Gaussian distribution is fully characterized by its variance, which we analytically relate to the spin diffusion constant and static spin susceptibility, comparing our prediction 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.