  Three-dimensional (3D) strongly correlated many-body systems, especially
their dynamics across quantum phase transitions, are prohibitively difficult to
be numerically simulated. We experimentally demonstrate that such complex
many-body dynamics can be efficiently studied in a 3D spinor Bose-Hubbard model
quantum simulator, consisting of antiferromagnetic spinor Bose-Einstein
condensates confined in cubic optical lattices. We find novel dynamics and
scaling effects beyond the scope of existing theories at superfluid-insulator
quantum phase transitions and highlight spin populations as a new observable to
probe the quantum critical dynamics. Our data indicate that the scaling
exponents are independent of the nature of the quantum phase transitions. We
also conduct numerical simulations in lower dimensions using time-dependent
Gutzwiller approximations, which qualitatively describe our observations.
