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We use unrestricted Hartree-Fock, density matrix renormalization group, andvariational projected entangled pair state calculations to investigate theground state phase diagram of the triangular lattice Hubbard model at "halfdoping" 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 thenon-interacting limit, and hence a weak-coupling instability towardsdensity-wave orders whose wavevectors are determined by Fermi surface nestingconditions. We find that at moderate to strong interaction strengths otherspatially-modulated orders arise, with wavevectors distinct from the nestingvectors. In particular, we identify a series closely-competing itinerantlong-wavelength magnetically ordered states, yielding to uniform ferromagneticorder at the largest interaction strengths. For half-hole doping and a similarrange of interaction strengths, our data indicate that magnetic orders are mostlikely absent.

Itinerant Magnetism in the Triangular Lattice Hubbard Model at Half-doping: Application to Twisted Transition-Metal Dichalcogenides