Flat-band ferromagnetism in a topological Hubbard model

TL;DR

This paper investigates the spin-wave excitations in a topological Hubbard model with flat bands, revealing gapless modes in Chern insulators and gapped modes in Z2 topological insulators, using a bosonization approach.

Contribution

It extends bosonization formalism to topological flat-band Hubbard models, analyzing their spin-wave spectra and topological distinctions.

Findings

Gapless spin-wave spectrum in correlated Chern insulators.

Gapped spin-wave spectrum in correlated Z2 topological insulators.

Effective boson model captures topological effects in flat-band systems.

Abstract

We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the \pi-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor \nu=1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation 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.