We perform a numerical study using both determinantal and constrain path Monte Carlo methods to investigate the magnetic and pairing properties of the single-band Hubbard model on the triangular lattice. We find that the system in the filling region
⟨n⟩=1.5−−1.85 shows a short-ranged ferromagnetic correlation, and the on-site Coulomb interaction tends to strengthen ferromagnetic fluctuation slightly. It is shown that the large density of states near the Van Hove singularity point plays an important role in the enhancement of ferromagnetic fluctuation. In the ferromagnetic region, we observe that the
f-wave pairing correlation tends to increase faster than other pairing correlations. However, it is subtle to stabilize the
f-wave pairing since the effective pairing interaction was found to be very small.
The density-matrix renormalization-group method is used to analyze how the nearest-neighbor repulsion
V added to the Hubbard model on a one-dimensional triangular lattice and a railway-trestle ${(t\ensuremath{-}t}^{\ensuremath{'}})$ model will affect the electron-correlation-dominated ferromagnetism arising from the interference (frustration). The obtained phase diagram shows that there is a region in the small-${t}^{\ensuremath{'}}$ side where the critical on-site repulsion above which the system becomes ferromagnetic is reduced when the off-site repulsion is introduced.
Abstract In order to analyse the lattice dependence of ferromagnetism in the two‐dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree‐Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non‐bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.