  Twisted bilayer transition metal dichalcogenides have emerged as important
model systems for the investigation of correlated electron physics because
their interaction strength, carrier concentration, band structure, and
inversion symmetry breaking are controllable by device fabrication, twist
angle, and most importantly, gate voltage, which can be varied in situ. The low
energy physics of some of these materials has been shown to be described by a
"moir\'e Hubbard model" generalized from the usual Hubbard model by the
addition of strong, tunable spin orbit coupling and inversion symmetry
breaking. In this work, we use a Hartree-Fock approximation to reach a
comprehensive understanding of the moir\'e Hubbard model on the mean field
level. We determine the magnetic and metal-insulator phase diagrams, and assess
the effects of spin orbit coupling, inversion symmetry breaking, and the
tunable van Hove singularity. We also consider the spin and orbital effects of
applied magnetic fields. This work provides guidance for experiments and sets
the stage for beyond mean-field calculations.
