2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25281We consider a deformed flat-band Hubbard model under a periodic boundary condition in arbitrary dimensions. We show that the ground state is only all-spin-up or -down state. We obtain upper and lower bounds of the one-magnon spin-wave energy with an arbitrary momentum. This dispersion relation is the same as that in the XXZ model in the certain parameter region. Therefore the spin wave has a finite energy gap. These results suggests the our model and the XXZ model.30 pages, 1 figureStrongly Correlated ElectronsMathematical Physicstext