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Itinerant magnetism in the triangular lattice Hubbard model at half-doping: Application to twisted transition-metal dichalcogenides

We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled pair state calculations to investigate the ground state phase diagram of the triangular lattice Hubbard model at "half doping" relative to single occupancy, i.e. at a filling of $(1\pm \frac{1}{2})$ electrons per site. The electron-doped case has a nested Fermi surface in the non-interacting limit, and hence a weak-coupling instability towards density-wave orders whose wavevectors are determined by Fermi surface nesting conditions. We find that at moderate to strong interaction strengths other spatially-modulated orders arise, with wavevectors distinct from the nesting vectors. In particular, we identify a series closely-competing itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.