Emergent Griffith's Phase in a Facilitated Rydberg Gas at Low Temperatures

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte-Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. We analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limit of low temperatures. As a result of the slow movement of atoms, excitations are locally constrained. While at finite temperatures the system displays an absorbing state phase transition, we show that this is replaced with an extended Griffith's phase in the frozen gas limit. Furthermore, we expand upon an existing Langevin equation to more accurately describe the density of Rydberg atoms in the frozen and finite temperature regimes.