Observation of a finite-energy phase transition in a one-dimensional quantum simulator

Abstract

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.

5+9 pages, 4+14 figures

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• Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature
• Mitigation of correlated readout errors without randomized measurements
• Efimov Effect in Long-range Quantum Spin Chains
• Stability of thermal equilibrium in long-range quantum systems
• Dynamic thermalization on noisy quantum hardware
• Emergence of topological states in relaxation dynamics of interacting bosons
• Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model
• Universal Relations in Long-range Quantum Spin Chains
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems