We investigate the role of momentum for the transport of magnetization in the spin-$1/2$ Heisenberg chain above the isotropic point at finite temperature and momentum. Using numerical and analytical approaches, we analyze the autocorrelations of density and current and observe a finite region of the Brillouin zone with diffusive dynamics below a cutoff momentum, and a diffusion constant independent of momentum and time, which scales inversely with anisotropy. Lowering the temperature over a wide range, starting from infinity, the diffusion constant is found to increase strongly while the cutoff momentum for diffusion decreases. Above the cutoff momentum diffusion breaks down completely.

• Received 17 July 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.250602