  We study numerically a disordered transverse-field Ising Hamiltonian with
long-range couplings. This model was recently investigated experimentally in a
trapped-ion quantum simulator and was found to exhibit features of many-body
localization at strong disorder. We use exact diagonalization to study the
collective state preservation and the eigenstate entanglement structure as a
function of both disorder strength and interaction range. Our numerical
results, using the same system sizes as the experiment, verify the observation
of many-body localization reported in the recent quantum simulation experiment,
and point to directions for future experiments.
