Subdiffusive front scaling in interacting integrable models

TL;DR

This paper demonstrates that certain initial states in interacting integrable models lead to subdiffusive transport with t^{1/3} scaling, challenging previous beliefs about the incompatibility of Tracy-Widom scaling with interactions.

Contribution

The study reveals that interacting integrable models can exhibit subdiffusive front scaling, specifically t^{1/3}, for a class of initial states including the domain wall, supported by numerical simulations.

Findings

Subdiffusive t^{1/3} scaling observed in spin, energy, and entanglement fronts.

Subdiffusive behavior persists across the entire anisotropy range in the XXZ chain.

Tracy-Widom scaling is compatible with interactions in integrable models.

Abstract

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.