Critically slow operator dynamics in constrained many-body systems

TL;DR

This paper investigates how conservation laws in constrained quantum systems, like dipole conservation, alter the typical operator spreading behavior, revealing a critical point with sub-ballistic dynamics and a localization transition.

Contribution

It introduces a new critical point in constrained many-body systems where operator growth transitions from ballistic to frozen, supported by numerical automaton circuit simulations.

Findings

Identification of a critical point with sub-ballistic operator spreading

Demonstration of a localization transition in dipole-conserving systems

Development of an effective biased random walk model for operator fronts

Abstract

The far-from-equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the ballistic spreading of initially local operators. Here, we show that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we study operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton chain. We identify a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase. This critical point is tied to an underlying localization transition and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times. We support our arguments numerically using classically simulable automaton circuits.