  We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in
the presence of an external transverse field to engineer a simulator of the
Dicke Hamiltonian, an iconic model in quantum optics which features a quantum
phase transition between a superradiant/ferromagnetic and a normal/paramagnetic
phase. We experimentally implement slow quenches across the quantum critical
point and benchmark the dynamics and the performance of the simulator through
extensive theory-experiment comparisons which show excellent agreement. The
implementation of the Dicke model in fully controllable trapped ion arrays can
open a path for the generation of highly entangled states useful for enhanced
metrology and the observation of scrambling and quantum chaos in a many-body
system.
