



02080nas a2200193   4500008004100000245009100041210006900132260001500201520147600216100002501692700001301717700001401730700001901744700001601763700002101779700002501800700002401825856003701849       2023                        eng d00aObservation of a finite-energy phase transition in a one-dimensional quantum simulator0 aObservation of a finiteenergy phase transition in a onedimension  c10/30/20233 a<p>One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to 23 spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.</p>1 aSchuckert, Alexander1 aKatz, Or1 aFeng, Lei1 aCrane, Eleanor1 aDe, Arinjoy1 aHafezi, Mohammad1 aGorshkov, Alexey, V.1 aMonroe, Christopher  uhttps://arxiv.org/abs/2310.19869