Slow dynamics and magnon bound states in the 2D long-range quantum Ising model

The dynamics of long-range quantum Ising models represents a current frontier in experimental physics, notably in trapped ions or Rydberg atomic systems. However, a theoretical description of these dynamics beyond 1D remains a significant challenge for conventional methods. Here, we address this challenge by means of neural quantum states to simulate global quenches from the fully polarized ferromagnetic state in the 2D quantum Ising model with power-law decaying interactions. From these numerically exact simulations, we find that the dynamics exhibit slow relaxation with long-lived oscillations. We explain this behavior through a theory for the formation of magnon bound states, which are generated, as we show, through effective attractive interactions between magnons that persist over several lattice sites due to the power-law nature of the interactions. Our results are readily observable in current quantum simulation platforms realizing long-range interacting models such as in Rydberg atomic systems.