Simulating the Temperature-Dependent Absorbing-State Phase Transition in a Rydberg Many-Body Facilitated Gas using Neural Networks

We investigate the many-body dynamics of driven dissipative Rydberg gases in the facilitation regime, where the emergence of self-organized criticality (SOC) has been experimentally observed [Helmrich et al., Nature 577 (2020)]. Using a graph neural network (GNN) approach we learn the time-dynamics operator of the open system at small and intermediate scale. This subsequently allows us to simulate and extrapolate the time evolution of the gas with particle numbers approaching those of the experimental realization. We consider the size distribution of scale-free avalanches of atomic excitations, one of the characteristics of SOC, as a function of the gas' temperature. We discuss the implications of this pertaining to the absorbing-state phase transition and its replacement by an extended Griffith's phase at low temperature.