Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays

Abstract: The Ising model serves as a canonical platform for exploring emergent symmetry in quantum critical systems. The critical point of the 1D Ising chain is described by a conformal Ising field theory, which remains integrable in the presence of a magnetic perturbation leading to massive particles associated with the exceptional Lie algebra $E_8$. Coupling two Ising chains in a ladder leads to an even richer $\mathcal{D}^{(1)}_8$ symmetry. Experimental signatures of the associated particle excitations have arguably been observed in scattering studies of the spin chain material CoNb$_2$O$_6$. Here, we probe these emergent symmetries in a Rydberg atom quantum processing unit, leveraging its tunable geometry to realize both chain and ladder configurations. We identify mass spectra consistent with $E_8$ and $\mathcal{D}^{(1)}_8$ symmetries at the respective critical points. Our results demonstrate the power of Rydberg platforms for investigating symmetry emergence in quantum many-body systems and provide a direct window into the interplay of confinement, geometry and criticality.