  Understanding quantum thermalization through entanglement build-up in
isolated quantum systems addresses fundamental questions on how unitary
dynamics connects to statistical physics. Here, we study the spin dynamics and
approach towards local thermal equilibrium of a macroscopic ensemble of S = 3
spins prepared in a pure coherent spin state, tilted compared to the magnetic
field, under the effect of magnetic dipole-dipole interactions. The experiment
uses a unit filled array of 104 chromium atoms in a three dimensional optical
lattice, realizing the spin-3 XXZ Heisenberg model. The buildup of quantum
correlation during the dynamics, especially as the angle approaches pi/2, is
supported by comparison with an improved numerical quantum phase-space method
and further confirmed by the observation that our isolated system thermalizes
under its own dynamics, reaching a steady state consistent with the one
extracted from a thermal ensemble with a temperature dictated from the system's
energy. This indicates a scenario of quantum thermalization which is tied to
the growth of entanglement entropy. Although direct experimental measurements
of the Renyi entropy in our macroscopic system are unfeasible, the excellent
agreement with the theory, which can compute this entropy, does indicate
entanglement build-up.
