  Quantum simulators have the potential to shed light on the study of quantum
many-body systems and materials, offering unique insights into various quantum
phenomena. While adiabatic evolution has been conventionally employed for state
preparation, it faces challenges when the system evolves too quickly or the
coherence time is limited. In such cases, shortcuts to adiabaticity, such as
spatiotemporal quenches, provide a promising alternative. This paper
numerically investigates the application of spatiotemporal quenches in the
two-dimensional transverse field Ising model with ferromagnetic interactions,
focusing on the emergence of the ground state and its correlation properties at
criticality when the gap vanishes. We demonstrate the effectiveness of these
quenches in rapidly preparing ground states in critical systems. Our
simulations reveal the existence of an optimal quench front velocity at the
emergent speed of light, leading to minimal excitation energy density and
correlation lengths of the order of finite system sizes we can simulate. These
findings emphasize the potential of spatiotemporal quenches for efficient
ground state preparation in quantum systems, with implications for the
exploration of strongly correlated phases and programmable quantum computing.
