Transport in a one-dimensional isotropic Heisenberg model at high temperature

Magnetization transport in a one-dimensional isotropic spin 1/2 Heisenberg model is studied. It is shown that in a nonequilibrium steady state at high temperature and constant small driving the magnetization current depends on the system length L as similar to 1/L-0.5, meaning that the diffusion constant diverges as similar to L-0.5. Spectral properties of a superoperator governing the relaxation towards a nonequilibrium steady state are also discussed.