Dynamical critical behavior of long-range spin models

Long range interacting spin models exhibit a variety of order-to-disorder phase transitions. We consider prototypical long-range spins models, and investigate dynamical properties of the order parameter as well as entanglement after a sudden quench in the Hamiltonian. The quench dynamics is studied through a combination of exact numerics and analytical calculations. We show that, depending on the nature of quench, different dynamical critical behavior arises. Specifically, we identify regimes when the stationary state at long times exhibits a non-thermal scaling behavior, and describe the signatures in the entanglement. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.