Quasiballistic transport and long-living fermionic excitations in long-range anisotropic Heisenberg model*

Purely ballistic transport is a rare feature even for integrable models. By numerically studying the Heisenberg chain with the power-law exchange, J∼1/r^α, where r is a distance, we show that for spin anisotropy Δ≈exp(-α+2) the system exhibits a quasiballistic spin transport and the presence of fermionic exictations which do not decay up to extremely long times ∼10³/J. This conclusion is reached on the base of the dynamics of spin domains, the dynamical spin conductivity, inspecting the matrix elements of the spin-current operator, and by the analysis of most conserved operators. Our results smoothly connects two models where fully ballistic transport is present: free particles with nearest-neighbor hopping and the isotropic Haldane-Shastry model.