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We consider an effective Hubbard model with spin- and direction-dependent complex hoppings t, applied to twisted homobilayer WSe₂ using a variational Monte Carlo approach. The electronic correlations are taken into account by applying the Gutzwiller on-site correlator as well as long-range Jastrow correlators subjected to noninteracting part being of Pfaffian form. Our analysis shows the emergence of the Mott insulating state at the critical value of Hubbard interaction U₂₁6. 5|t|7|t| estimated by extrapolating the density-density equal-time two-particle Green's functions. The signatures of an intermediate insulating phase between U₂₁ and U₂₂9. 5|t|10|t| are also discussed. Furthermore, we report the formation of the 120^ in-plane N\'eel state indicated by the detailed analysis of the spin-spin correlation functions. As shown, switching between antiferromagnetic phases characterized by opposite chirality could be experimentally realized by the change of perpendicular electric field. In a proper range of electric fields, also a transition to the in-plane ferromagnetic state appears.
Biborski et al. (Mon,) studied this question.