Anomalous nonequilibrium current fluctuations in the Heisenberg model

TL;DR

This paper investigates the unusual fluctuation behavior of spin currents in a one-dimensional anisotropic Heisenberg model out of equilibrium, revealing non-diffusive characteristics in higher-order current cumulants.

Contribution

It provides the first numerical analysis of large-deviation properties of spin current cumulants in the nonequilibrium Heisenberg model, highlighting anomalous fluctuation scaling.

Findings

First two cumulants scale diffusively with system size

Third and fourth cumulants do not scale diffusively

Model exhibits non-ordinary diffusive spin conduction

Abstract

We study fluctuation properties of a one-dimensional anisotropic Heisenberg model out of equilibrium, focusing in particular on the gapped regime. Within the open-system setting we study large-deviation properties of the spin current. Numerically evaluating the first four current cumulants in a nonequilibrium stationary state at high energies, we find that the first two cumulants scale with the system size in a diffusive way, while the 3rd and the 4th cumulants do not. This means that the model is not an ordinary diffusive spin conductor.