Moiré Kanamori-Hubbard model for transition metal dichalcogenide homobilayers

Ab initio and continuum model studies predicted that the $\mathrm{\ensuremath{\Gamma}}$ valley transition metal dichalcogenide (TMD) homobilayers could simulate the conventional multiorbital Hubbard model on the moir\'e honeycomb lattice. Here, we perform the Wannierization starting from the continuum model and show that a more general moir\'e Kanamori-Hubbard model emerges, beyond the extensively studied standard multiorbital Hubbard model, which can be used to investigate the many-body physics in the $\mathrm{\ensuremath{\Gamma}}$ valley TMD homobilayers. Using the unrestricted Hartree-Fock and Lanczos techniques, we study these half-filled multiorbital moir\'e bands. By constructing the phase diagrams we predict the presence of an antiferromagnetic state and in addition we found unexpected and dominant states, such as a $S=1$ ferromagnetic insulator and a charge density wave state. Our theoretical predictions made using this model can be tested in future experiments on the $\mathrm{\ensuremath{\Gamma}}$ valley TMD homobilayers.