  We theoretically consider two-dimensional moir\'e transition metal
dichalcogenide (TMD) bilayers, which are strongly correlated in the sense that
the on-site Coulomb interaction is comparable to or larger than the hopping
kinetic energy between the moir\'e lattice sites. The system accommodates many
symmetry-broken ground states both in charge and isospin sectors at various
commensurate rational fillings such as 1/2, 1/3, 1/4, 2/3, etc. We investigate
two complementary important aspects of the dependence of the symmetry breaking
on (1) the range of the electron-electron interaction, which can in principle
be experimentally controlled by the nearby gates and the dielectric
environment, and (2) temperature, which could thermally suppress the symmetry
breaking above a critical temperature. Experimental implications of the theory
are discussed.
