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.