Coexistence of anomalous and normal diffusion in integrable Mott insulators

We study the finite-momentum spin dynamics in the one-dimensional X-0.16em0exX-0.16em0exZ 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.