Variational Monte-Carlo Approach for Hubbard Model Applied to Twisted Bilayer WSe_2 at Half-Filling

We consider an effective Hubbard model with spin- and direction-dependent complex hoppings t, applied to twisted homobilayer WSe_2 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 Mott insulating state at critical value of Hubbard interaction U_c1≈ 6.5|t|÷7|t| estimated by extrapolating the density-density equal-time two-particle Green's functions. The signatures of an intermediate insulating phase between U_c1 and U_c2≈9.5|t|÷10|t| are also discussed. Furthermore, we report the formation of the 120^∘ in-plane Néel 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 proper range of electric fields also a transition to in-plane ferromagnetic state appears.