Subdiffusive front scaling in interacting integrable models

Understand

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.