Investigating localization properties of interacting disordered systems plays a crucial role in understanding thermalization and its absence in closed quantum systems. However, simulating such systems on classical computers is challenging due to their complexity. In this work we propose a method to realize $S=1/2$ and 1 quantum spin models with quasiperiodic interactions using Rydberg atoms by utilizing the high tunability of the atoms' spatial positions. We also perform numerical calculations and show that these models host a many-body critical regime, which differs from the ergodic and many-body localized regimes.

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• Cold atoms & matter waves
• Eigenstate thermalization
• Many-body localization
• Rydberg gases
• Quantum spin models
• XY model