Identifying phase boundaries of two-dimensional atom arrays with Rydberg blockade effect: a dual-order-parameter method

Abstract：Rydberg atom arrays with the blockade effect provide a controllable platform for studying nonequilibrium quantum many-body physics. The uniform, antiferromagnetic, oscillatory, and bistable phases in Rydberg atom systems are important for understanding driven-dissipative phase transition. They are also relevant to quantum simulation and quantum information processing, so identifying their phase boundaries is necessary for the controlled use of these phases. Identifying the boundaries among these phases remains challenging because no single order-parameter can characterize all phases within a unified framework. One of the reasons is that the dynamical behavior of the bistable phases depends on the initial Rydberg-state population, which leads to either a bistable state between the uniform phase and the oscillatory phase or a bistable state between the uniform phase and the antiferromagnetic phase. In this paper, a dual order-parameter method for phase identification is proposed for Rydberg blockade atom arrays. A new ratio parameter, which is defined to describe the difference of initial Rydberg-state population between neighboring sublattices, is used to distinguish different phase. The results show our method can identify effectively the phase boundaries of the two-dimensional Rydberg blockade atom arrays even if the mean-field approximation based on the Lindblad master equation is used.The method may be used for a dynamical phase transition in non-equilibrium many-body systems.