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We show that any interacting integrable model possesses a class of initialstates for which the leading corrections to ballistic transport aresubdiffusive rather than diffusive. These initial states are natural to realizeexperimentally and include the domain wall initial condition that has been theobject of much recent scrutiny. Upon performing numerical matrix product statesimulations in the spin-$1/2$ XXZ chain, we find that such states can exhibitsubdiffusive $t^{1/3}$ scaling of fronts of spin, energy and entanglemententropy across the entire range of anisotropies. This demonstrates thatTracy-Widom scaling is not incompatible with model interactions, as waspreviously believed.

Subdiffusive front scaling in interacting integrable models