Emergent Kinetic Constraints and Subspace Fragmentation in Rydberg Arrays

TL;DR

This paper investigates how variable detuning in Rydberg atom arrays leads to fragmented Hilbert subspaces, revealing emergent kinetic constraints that govern nonergodic many-body dynamics beyond the PXP model.

Contribution

It systematically uncovers the dependence of Hilbert space fragmentation on detuning and interaction, introducing an auxiliary fermion approach to understand emergent kinetic constraints.

Findings

Hilbert subspaces are strongly fragmented with size-dependent scaling behaviors.

Emergent kinetic constraints are revealed through an auxiliary fermion description.

The study extends understanding of nonergodic dynamics beyond the PXP model.

Abstract

In a strongly interacting Rydberg atom array, the dynamics are often constrained to the decoupled Hilbert subspaces, representing an intriguing paradigm for nonergodicity. By considering a variable detuning of the global Rydberg coupling, we show that, not only is the existence of these Hilbert subspaces dependent on the interplay of detuning and interaction, but they are also strongly fragmented, with the fragment dimensions exhibiting various scaling behaviors with increasing system size. The resulting constrained dynamics of the system are thus governed by the dimension and connectivity of these fragments. We then adopt an auxiliary fermion description to reveal the underlying emergent kinetic constraints for the subspace fragmentation and fragment-confined dynamics. Our results provide a systematic understanding of Hilbert-space fragmentation in Rydberg arrays, and shed light on engineering nonergodic many-body dynamics beyond the PXP model.