  Understanding the many-body dynamics of isolated quantum systems is one of
the central challenges in modern physics. To this end, the direct experimental
realization of strongly correlated quantum systems allows one to gain insights
into the emergence of complex phenomena. Such insights enable the development
of theoretical tools that broaden our understanding. Here, we theoretically
model and experimentally probe with Ramsey spectroscopy the quantum dynamics of
disordered, dipolar-interacting, ultracold molecules in a partially filled
optical lattice. We report the capability to control the dipolar interaction
strength, and we demonstrate that the many-body dynamics extends well beyond a
nearest-neighbor or mean-field picture, and cannot be quantitatively described
using previously available theoretical tools. We develop a novel cluster
expansion technique and demonstrate that our theoretical method accurately
captures the measured dependence of the spin dynamics on molecule number and on
the dipolar interaction strength. In the spirit of quantum simulation, this
agreement simultaneously benchmarks the new theoretical method and verifies our
microscopic understanding of the experiment. Our findings pave the way for
numerous applications in quantum information science, metrology, and condensed
matter physics.
