Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model

TL;DR

This paper investigates the spin-wave excitations in the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice, revealing the spectrum's structure and effects of various energy offsets using a bosonization approach.

Contribution

It introduces a bosonization scheme for flat-band Chern insulators to analyze spin-wave spectra in the Haldane-Hubbard model, including effects of energy offsets and phase stability.

Findings

The spin-wave spectrum has two branches with a Goldstone mode and Dirac points.

Energy offsets open gaps at K and K' points in the spectrum.

Staggered on-site energy may cause instability in the ferromagnetic phase.

Abstract

We study the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice within a bosonization scheme for flat-band Chern insulators, focusing on the calculation of the spin-wave excitation spectrum. We consider the Haldane-Hubbard model with the noninteracting lower bands in a nearly-flat band limit, previously determined for the spinless model, and at 1/4-filling of its corresponding noninteracting limit. Within the bosonization scheme, the Haldane-Hubbard model is mapped into an effective interacting boson model, whose quadratic term allows us to determine the spin-wave spectrum at the harmonic approximation. We show that the excitation spectrum has two branches with a Goldstone mode and Dirac points at center and at the K and K' points of the first Brillouin zone, respectively. We also consider the effects on the spin-wave spectrum due to an energy offset in the on-site Hubbard repulsion energies and due to the presence of an staggered on-site energy term, both quantities associated with the two triangular sublattices. In both cases, we find that an energy gap opens at the K and K' points. Moreover, we also find some evidences for an instability of the flat-band ferromagnetic phase in the presence of the staggered on-site energy term. We provide some additional results for the square lattice topological Hubbard model previous studied within the bosonization formalism and comment on the differences between the bosonization scheme implementation for the correlated Chern insulators on both square and honeycomb lattices.