Itinerant Ferromagnetism in the Triangular Lattice Hubbard Model

The Hubbard model was initially proposed to explain kinetic ferromagnetism (FM) in transition metals. While FM is indeed stabilized at infinite onsite Coulomb repulsion U (as pointed out by Nagaoka and Thouless for the case of one hole at half filling), this is not the case at finite U and filling for the bipartite square (relevant to materials such as the cuprates) and cubic lattices. Frustration requires that these qualitative results be revisited, which motivates our present study. We explore the phase diagram of the Hubbard model above half filling (f=1) on the frustrated triangular lattice and demonstrate its tendency to stabilize a weak but robust FM ground state. In contrast to previous mean field approaches, our many-body calculations, based on the density matrix renormalization group, reveal that the FM is stabilized in a relatively narrow region in phase space, a finding of possible relevance to recent transition metal dichalcogenide (moire) based experiments. We estimate the critical U between the unpolarized paramagnet and FM phases, finding the latter to have an itinerant character. We then seek an explanation of the kinetic origin of FM within the Stoner theory, based on the occurrence of a van Hove singularity at f=1.5, and conclude by constructing a variational ansatz for the ground state wavefunction.