Kardar-Parisi-Zhang Universality in the Infinite Temperature spin-half Heisenberg Chain

There are two simple paradigms of how conserved quantities transport through a system: thermalizing systems with effectively random collisions in the system leading to diffusion, and particles moving freely in a material giving rise to ballistic transport. In the spin-half XXZ model in one dimension, both of these behaviors have been shown rigorously. Recent studies have suggested at the isotropic point of the model, the spin-half Heisenberg model, there is a third behavior at infinte temperature given by the stochastic classical Kardar-Parisi-Zhang (KPZ) universality class. In this work, I computed the dynamical structure factor at infinite temperature using matrix product states for the spin-half Heisenberg, and show that it exhibits the scaling function from the KPZ universality class, strengthening the claim that KPZ dynamics are present in quantum spin systems.