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The recent rapid experimental advancement in the engineering of quantummany-body systems opens the avenue to controlled studies of fundamental physicsproblems via digital or analog quantum simulations. Here, we systematicallyanalyze the capability of analog ion traps to explore relativistic mesonspectra on current devices. We focus on the E_8 quantum field theory regime,which arises due to longitudinal perturbations at the critical point of thetransverse-field Ising model. As we show through exact numerics, forsufficiently strong long-range suppression in experimentally accessible spinchain models, absorption spectroscopy allows for the identification of thelow-lying meson excitations with a good degree of accuracy even for smallsystem sizes. Our proposal thus opens a way for probing salient features ofquantum many-body systems reminiscent of meson properties in high-energyphysics.

Relativistic meson spectra on ion-trap quantum simulators