  Simulating the real-time evolution of quantum spin systems far out of
equilibrium poses a major theoretical challenge, especially in more than one
dimension. We experimentally explore the dynamics of a two-dimensional Ising
spin system with transverse and longitudinal fields as we quench it across a
quantum phase transition from a paramagnet to an antiferromagnet. We realize
the system with a near unit-occupancy atomic array of over 200 atoms obtained
by loading a spin-polarized band insulator of fermionic lithium into an optical
lattice and induce short-range interactions by direct excitation to a low-lying
Rydberg state. Using site-resolved microscopy, we probe the correlations in the
system after a sudden quench from the paramagnetic state and compare our
measurements to exact calculations in the regime where it is possible. We
achieve many-body states with longer-range antiferromagnetic correlations by
implementing a near-adiabatic quench and study the buildup of correlations as
we cross the quantum phase transition at different rates.
