# Griffiths Phase in a Facilitated Rydberg Gas at Low Temperature

## TL;DR

This paper investigates the dynamics of facilitated Rydberg gases at different temperatures, revealing a Griffiths phase at low temperatures and phase transition behaviors at high temperatures, with implications for understanding many-body quantum systems.

## Contribution

It introduces a detailed analysis of Rydberg facilitation dynamics across temperature regimes, highlighting the emergence of a Griffiths phase and extending Langevin models for better accuracy.

## Key findings

- At high temperatures, a homogeneous mean-field behavior is observed.
- In frozen gases, a Griffiths phase replaces the traditional phase transition.
- The extended Langevin equation improves modeling of Rydberg atom density.

## Abstract

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. In this paper, we analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. While in the high-temperature limit a homogeneous mean-field behaviour is recovered, characteristic effects of heterogeneity can be seen in a frozen gas. At large temperatures the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erd\"os-Renyi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erd\"os-Renyi network taking into account Rydberg blockade. Furthermore, we expand upon an existing macroscopic Langevin equation to more accurately describe the density of Rydberg atoms in the frozen and finite temperature regimes.