Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space

TL;DR

This paper investigates the origin of many-body scars in Rydberg atom models by deforming the graph adjacency matrix of the PXP model, revealing hypercube structures and their role in wavefunction revivals.

Contribution

It introduces a family of deformed models based on hypergrid subgraphs that explain the emergence and robustness of many-body scars in Rydberg systems.

Findings

Hypercube and hypergrid graph structures underpin scarred wavefunctions.

Deformations can enhance or relax constraints, affecting scar robustness.

The hypercube model captures key features of scars in the PXP model.

Abstract

Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in non-integrable quantum systems. Here we explore the origin of scarred wavefunction revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model - the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.