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We study the flat-band ferromagnetic phase of a topological Hubbard modelwithin a bosonization formalism and, in particular, determine the spin-waveexcitation spectrum. We consider a square lattice Hubbard model at 1/4-fillingwhose free-electron term is the \pi-flux model with topologically nontrivialand nearly flat energy bands. The electron spin is introduced such that themodel either explicitly breaks time-reversal symmetry (correlated flat-bandChern insulator) or is invariant under time-reversal symmetry (correlatedflat-band $Z_2$ topological insulator). We generalize for flat-band Chern andtopological insulators the bosonization formalism [Phys. Rev. B 71, 045339(2005)] previously developed for the two-dimensional electron gas in a uniformand perpendicular magnetic field at filling factor \nu=1. We show that, withinthe bosonization scheme, the topological Hubbard model is mapped into aneffective interacting boson model. We consider the boson model at the harmonicapproximation and show that, for the correlated Chern insulator, the spin-waveexcitation spectrum is gapless while, for the correlated topological insulator,gapped. We briefly comment on the possible effects of the boson-boson(spin-wave--spin-wave) coupling.

Flat-band ferromagnetism in a topological Hubbard model