High-temperature dynamical structure factor for spin-half Heisenberg chain

We compute the dynamical structure factor (DSF) for the isotropic spin-half Heisenberg chain from high to low temperatures using the the DMRG on top of the exponential tensor renormalization group (XTRG) for thermal states. We find a sharp upper bound to the spinon continuum for all temperatures that is qualitatively similar to the DSF at low temperature. Translated to real-time, the system features a light cone even at infinite temperature for shorter time scales. For intermediate to long time scales we observe strong evidence for a transition to superdiffusive behavior that is described by a dynamical exponent z=1.5 in between diffusive (z=1) and ballistic (z=2) behavior. These findings are in good agreement with recent neutron scattering experiments on effective spin-half chains in the rare earth perovskite YbAlO₃.