Continuous Symmetry Breaking in a Trapped-Ion Crystal*

One-dimensional systems can host quantum phases of matter with macroscopic order if the interaction range between the particles is sufficiently long. In most physical systems, however, the interactions are short-range, hindering the emergence of such phases in one dimension in general. Here we use a one-dimensional trapped-ion quantum simulator to prepare a many-body state in a Continuous Symmetry Breaking (CSB) phase with long-range spin order. Our preparation relies on simultaneous control over an array of 23 tightly focused individually addressing laser beams, generating long-range spin-spin interactions. We also observe a critical XY phase when the long-range interactions are frustrated. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.