  Many of the important phases observed in twisted transition metal
dichalcogenide homobilayers are driven by short-range interactions, which
should be captured by a local tight binding description since no Wannier
obstruction exists for these systems. Yet, published theoretical descriptions
have been mutually inconsistent, with honeycomb lattice tight binding models
adopted for some twist angles, triangular lattice models adopted for others,
and with tight binding models forsaken in favor of band projected continuum
models in many numerical simulations. Here, we derive and study a minimal model
containing both honeycomb orbitals and a triangular site that represents the
band physics across a wide range of twist angles. The model provides a natural
basis to study the interplay of interaction and topology in these
heterostructures. It elucidates from generic features of the bilayer the
sequence of Chern numbers occurring as twist angle is varied, and the
microscopic origin of the magic angle at which flat-band physics occurs. At
integer filling, the model successfully captures the Chern ferromagnetic and
van-Hove driven antiferromagnetic insulators experimentally observed for small
and large angles, respectively, and allows a straightforward calculation of the
magneto-electric properties of the system.
