Non-Markovian dynamics of the open Dicke model beyond the mean-field limit

We study the zero-temperature steady-state superradiant phase transition in the open Dicke model in the presence of non-Markovian local dephasing baths. The mean-field dynamics is shown to exhibit initial state dependence in the long time limit in some parameter regimes. We develop an analytical framework to describe the dynamics incorporating effects beyond mean-field, and show numerical evidence of its validity.