  The Hubbard model, first formulated by physicist John Hubbard in the 1960s,
is a simple theoretical model of interacting quantum particles in a lattice.
The model is thought to capture the essential physics of high-temperature
superconductors, magnetic insulators, and other complex emergent quantum
many-body ground states. Although the Hubbard model is greatly simplified as a
representation of most real materials, it has nevertheless proved difficult to
solve accurately except in the one-dimensional case. Physical realization of
the Hubbard model in two or three dimensions, which can act as quantum
simulators, therefore have a vital role to play in solving the
strong-correlation puzzle. Here we obtain a quantum phase diagram of the
two-dimensional triangular lattice Hubbard model by studying angle-aligned
WSe2/WS2 bilayers, which form moir\'e superlattices because of the difference
in lattice constant between the two two-dimensional materials. We probe both
charge and magnetic properties of the system by measuring the dependence of
optical response on out-of-plane magnetic field, and on gate-tuned carrier
density. At half filling of the first hole moir\'e superlattice band, we
observe a Mott insulating state with antiferromagnetic Curie-Weiss behavior as
expected for a Hubbard model in the strong interaction regime. Past half
filling, our experiment suggests an antiferromagnetic to paramagnetic quantum
phase transition near 0.6 filling. Our results establish a new solid-state
platform based on moir\'e superlattices which can be used to simulate
outstanding problems in strong correlation physics that are manifested by
triangular lattice Hubbard models.
