Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and Finite-Time Scaling

Rydberg atoms have become an ideal platform for studying isolated quantum many-body systems. By controlling the laser detuning and the inter-atomic distance, one can investigate diverse critical phenomena, in particular, the commensurate-incommensurate quantum phase transitions. Our approach involves numerical simulation of critical real-time dynamics within non-equilibrium chains of Rydberg atoms. Utilizing the time-evolving block decimation algorithm, we decode the intricacies of the commensurate-incommensurate phase transition via the application of the Kibble-Zurek mechanism and Finite-Time Scaling. We study the isolated conformal points surrounded by the new chiral quantum phase transition types with an effective blockade model where a constraint of no double occupancy replaces the short-distance repulsions. Combining the Kibble-Zurek mechanism with the Finite-Time Scaling theory, we extract all major critical exponents: ν, z and β. The implications of the finite-size effect will be briefly discussed.