Scalable Spin Squeezing in Power-Law Interacting XXZ Models with Disorder

Abstract: While spin squeezing has been traditionally considered in all-to-all interacting models, recent works have shown that spin squeezing can occur in systems with power-law interactions, leading to direct testing in Rydberg atoms, trapped ions, ultracold atoms and nitrogen vacancy (NV) centers in diamond. For the latter, Wu. et al. Nature 646 (2025) demonstrated that spin squeezing is heavily affected by positional disorder, reducing any capacity for a practical squeezing advantage, which requires scalability with the system size. In this Letter we explore the robustness of spin-squeezing in two-dimensional lattices with a fraction of unoccupied lattice sites. Using semi-classical modeling, we demonstrate the existence of scalable squeezing in power-law interacting XXZ models up to a disorder threshold, above which squeezing is not scalable. We produce a phase diagram for scalable squeezing, and explain its absence in the aforementioned NV experiment. Our work illustrates the maximum disorder allowed for realizing scalable spin squeezing in a host of quantum simulators, highlights a regime with substantial tolerance to disorder, and identifies controlled defect creation as a promising route for scalable squeezing in solid-state systems.