Anomalous Subdiffusion from Subsystem Symmetries

Understand

We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement.

• We provide a partial characterization of these "automaton" quantum circuits, and use them to study operator growth, information spreading, and local charge relaxation in quantum dynamics with subsystem symmetries, which we define as overlapping symmetries that act on lower-dimensional submanifolds.
• With these symmetries, we discover the anomalous subdiffusion of conserved charges; that is, the charges spread slower than diffusion in the dimension of the subsystem symmetry.
• By studying an effective operator hydrodynamics in the presence of these symmetries, we predict the charge autocorrelator to decay ($i$) as $\log(t)/\sqrt{t}$ in two dimensions with a conserved $U(1)$ charge along intersecting \emph{lines}, and ($ii$) as $1/t^{3/4}$ in three spatial dimensions with intersecting \emph{planar} $U(1)$ symmetries.