  The recent rapid experimental advancement in the engineering of quantum
many-body systems opens the avenue to controlled studies of fundamental physics
problems via digital or analog quantum simulations. Here, we systematically
analyze the capability of analog ion traps to explore relativistic meson
spectra on current devices. We focus on the E_8 quantum field theory regime,
which arises due to longitudinal perturbations at the critical point of the
transverse-field Ising model. As we show through exact numerics, for
sufficiently strong long-range suppression in experimentally accessible spin
chain models, absorption spectroscopy allows for the identification of the
low-lying meson excitations with a good degree of accuracy even for small
system sizes. Our proposal thus opens a way for probing salient features of
quantum many-body systems reminiscent of meson properties in high-energy
physics.
