Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems

TL;DR

This paper investigates how operators spread and broaden in interacting integrable systems, revealing that quasiparticle density fluctuations cause diffusive broadening of the operator front, a phenomenon also present in non-integrable systems.

Contribution

The paper derives a general expression for the front-broadening rate in interacting integrable models and explicitly applies it to a specific model, enhancing understanding of operator spreading mechanisms.

Findings

Operator fronts propagate ballistically with velocity set by quasiparticles.

Density fluctuations induce diffusive broadening of the operator front.

The derived broadening rate applies broadly to integrable models.

Abstract

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in non-integrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.