Coexistence of Anomalous and Normal Diffusion in Integrable Mott   Insulators
  We study the finite-momentum spin dynamics in the one-dimensional XXZ spin chain within the Ising-type regime at high temperatures using density autocorrelations within linear response theory and real-time propagation of nonequilibrium densities. While for the nonintegrable model results are well consistent with normal diffusion, the finite-size integrable model unveils the coexistence of anomalous and normal diffusion in different regimes of time. In particular, numerical results show a Gaussian relaxation at smallest nonzero momenta which we relate to nonzero stiffness in a grand canonical ensemble. For larger but still small momenta normal-like diffusion is recovered. Similar results for the model of impenetrable particles also help to resolve rather conflicting conclusions on transport in integrable Mott insulators. 
R. Steinigeweg, J. Herbrych, P. Prelov\v{s}ek, M. Mierzejewski
cond-mat.str-el