Disorder induced transition in the scalable spin squeezing of power-law interacting XXZ models

While spin squeezing has been traditionally considered in all-to-all interacting models, recent works have shown that scalable spin squeezing is possible in systems with power-law interactions, leading to direct testing in Rydberg atoms, trapped ions, ultracold atoms and nitrogen vacancy centers in diamond. For the latter, squeezing is significantly impacted by positional disorder. In this work we explore the robustness of spin-squeezing in regular lattices with a fraction of unoccupied lattice sites (holes). We demonstrate the existence of scalable squeezing in power-law interacting XXZ models up to a disorder threshold, above which squeezing is not scalable. Using semi-classical modelling, we extract a diverging time-scale near the transition, indicating a potential disorder-induced squeezing phase transition. Our work illustrates a minimal disorder requirement for realizing scalable spin squeezing in a host of quantum simulators.