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Twisted bilayer transition metal dichalcogenides have emerged as importantmodel systems for the investigation of correlated electron physics becausetheir interaction strength, carrier concentration, band structure, andinversion symmetry breaking are controllable by device fabrication, twistangle, and most importantly, gate voltage, which can be varied in situ. The lowenergy 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 theaddition of strong, tunable spin orbit coupling and inversion symmetrybreaking. In this work, we use a Hartree-Fock approximation to reach acomprehensive understanding of the moir\'e Hubbard model on the mean fieldlevel. We determine the magnetic and metal-insulator phase diagrams, and assessthe effects of spin orbit coupling, inversion symmetry breaking, and thetunable van Hove singularity. We also consider the spin and orbital effects ofapplied magnetic fields. This work provides guidance for experiments and setsthe stage for beyond mean-field calculations.

Hartree-Fock study of the moir\'e Hubbard model for twisted bilayer transition metal dichalcogenides