Non-ergodic quantum operator dynamics from causal constraints

Abstract

This paper explores a route to non-ergodic quantum dynamics where algebraic restrictions in operator space arise from local constraints on the causal light cone. We model this through tri-partite unitaries (we dub 'walls') that permanently arrest local operator spreading in periodic time-evolution. We show that the structure of the resulting causally independent subsystems can be understood rigorously through the invariance of embedded operator algebras (ie. super-operator symmetries). Our work involves a detailed study of local conserved quantities and generalisation to time-dependent dynamics. Using representation theory, the general form of wall gates is derived from the unitary automorphism group of the embedded algebra with links to quantum error-correcting codes. From the point of view of operator spreading, our theory is a minimal model for non-ergodic quantum circuit dynamics and we explore its effects on probes of many-body quantum chaos. We prove an entanglement area law due to causal constraints and discuss its stability against local measurements. In a random unitary ensemble with causally independent subsystems, we compare spectral correlations with the universal (chaotic) ensemble using the spectral form factor. Our results offer a rigorous understanding of locally constrained quantum dynamics from a quantum information perspective.