Anomalous nonequilibrium current fluctuations in the Heisenberg model
  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. 
Marko Znidaric
cond-mat.str-el cond-mat.stat-mech quant-ph