Eigenstate thermalization and the butterfly effect in simple kinetically constrained models
We introduce and explore the properties of a family of simple Floquet systems in which many-body eigenstates and dynamics can be efficiently classically computed. These models consist of repeatedly applied unitary gates, which are chosen to leave the dynamics "classical" (and therefore tractable) in a special basis; the nontrivial dynamics of these models stems from kinetic constraints. One of these models is a minimal example of an interacting integrable model: we show that, despite the integrability of this model, physical perturbations exhibit a butterfly effect with a butterfly "cone" analogous to chaotic systems, and physical observables obey the eigenstate thermalization hypothesis. We also find models that are neither chaotic nor integrable in the usual sense. Instead, in these models, perturbations spread along spacetime fractals.