Algebraic law of local correlations in a driven Rydberg atomic system

TL;DR

This paper explores how antiferromagnetic correlations develop in a driven Rydberg atomic system, revealing a universal superposition principle for correlation buildup that is robust across various geometries and protocols.

Contribution

It introduces a superposition law for correlation propagation in quantum simulators, supported by analytical and numerical evidence across different lattice configurations.

Findings

AF correlation magnitude follows a universal superposition principle

Superposition law is robust against geometry and protocol variations

Quantitative agreement between Magnus expansion and simulations

Abstract

Understanding the mechanism behind the buildup of inner correlations is crucial for studying nonequilibrium dynamics in complex, strongly interacting many-body systems. Here we investigate both analytically and numerically the buildup of antiferromagnetic (AF) correlations in a dynamically tuned Ising model with various geometries, realized in a Rydberg atomic system. Through second-order Magnus expansion (ME), we demonstrate quantitative agreement with numerical simulations for diverse configurations including $2 \times n$ lattice and cyclic lattice with a star. We find that the AF correlation magnitude at fixed Manhattan distance obeys a universal superposition principle: It corresponds to the algebraic sum of contributions from all shortest paths. This superposition law remains robust against variations in path equivalence, lattice geometries, and quench protocols, establishing a new paradigm for correlation propagation in quantum simulators.