Subdiffusive front scaling in interacting integrable models

We show that any interacting integrable model possesses a class of initial states for which the leading corrections to ballistic transport are subdiffusive rather than diffusive. These initial states are natural to realize experimentally and include the domain wall initial condition that has been the object of much recent scrutiny. Upon performing numerical matrix product state simulations in the spin-$1/2$ XXZ chain, we find that such states can exhibit subdiffusive $t^{1/3}$ scaling of fronts of spin, energy and entanglement entropy across the entire range of anisotropies. This demonstrates that Tracy-Widom scaling is not incompatible with model interactions, as was previously believed.