The peculiar effect of electron correlation in multiband systems is illustrated for the recently proposed ferromagnetism in a Hubbard model having flat bands. Depsite the flatness of the band, an acoustic spin-wave mode with a finite stiffness exists along with optical modes below a Stoner gap. The relevant energy (gap and stiffness) transmutes from the Hubbard U in the weak-coupling limit to t (transfer integral) in the strong-coupling limit. This implies a stable itinerant ferromagnetism with finite band widths.
Using equations of motion of connected Green functions the Hubbard III approximation is reexamined. It is shown that two important higher-order correlation effects are neglected in the Hubbard III treatment. One is bandwidth correction, the other is band-shift correction. These two corrections make important effects to the metal-insulator transition and spontaneous ferromagnetism in the Hubbard model. Due to the bandwidth correction the critical value of Uc in the metal-insulator transition decreases from 3/2W(W represents Bloch bandwidth) in the Hubbard III approximation to 0.67W, which approaches significantly the critical value of 0.5W by the quantum Monte Carlo simulation, while the band-shift correction leads to a ferromagnetic solution missed in the Hubbard III approximation in the limit of $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty},$ which is in qualitative agreement with the conclusion that the Hubbard model can describe the ferromagnetism resulted from the spectral density method and the quantum Monte Carlo simulation. Our studies show that the higher-order correlation effects play an important role in describing the properties of the strongly correlated systems.
We study a ferromagnetic instability in a doped single-band Hubbard model by means of dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations. Examining the effect of the strong correlations in the system on the hypercubic and Bethe lattice, we find that the ferromagnetically ordered state appears in the former, while it does not in the latter. We also reveal that the ferromagnetic order is more stable in the case that the noninteracting density of states (DOS) exhibits a slower decay in the high-energy region. The present results suggest that, in the strong-coupling regime, the high-energy part of DOS plays an essential role for the emergence of the ferromagnetically ordered state, in contrast to the Stoner criterion justified in the weak-interaction limit.