  We theoretically propose and experimentally demonstrate the use of motional
sidebands in a trapped ensemble of $^{87}$Rb atoms to engineer tunable
long-range XXZ spin models. We benchmark our simulator by probing a
ferromagnetic to paramagnetic dynamical phase transition in the
Lipkin-Meshkov-Glick (LMG) model, a collective XXZ model plus additional
transverse and longitudinal fields, via Rabi spectroscopy. We experimentally
reconstruct the boundary between the dynamical phases, which is in good
agreement with mean-field theoretical predictions. Our work introduces new
possibilities in quantum simulation of anisotropic spin-spin interactions and
quantum metrology enhanced by many-body entanglement.
