Ferromagnetism and spin excitations in topological Hubbard models with a flat band

Abstract

We study the spin-1 excitation spectra of the flatband ferromagnetic phases in interacting topological insulators. As a paradigm, we consider a quarter filled square lattice Hubbard model whose free part is the π flux state with topologically nontrivial and nearly-flat electron bands, which can realize either the Chern or Z2 Hubbard model. By using the numerical exact diagonalization method with a projection onto the nearly-flat band, we obtain the ferromagnetic spin-1 excitation spectra for both the Chern and Z2 Hubbard models, consisting of spin waves and Stoner continuum. The spectra exhibit quite distinct dispersions for both cases, in particular the spin wave is gapless for the Chern Hubbard model, while gapped for the Z2 Hubbard model. Remarkably, in both cases, the nonflatness of the free electron bands introduces dips in the lower boundary of the Stoner continuum. It significantly renormalizes the energies of the spin waves around these dips downward and leads to roton-like spin excitations. We elaborate that it is the softening of the roton-like modes that destabilizes the ferromagnetic phase, and determine the parameter region where the ferromagnetic phase is stable. arXiv:1810.11986v2 [cond-mat.str-el]

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

“…[38]). Such a scenario agrees with more recently numerical results for the square lattice π-flux model in the nearly-flat band limit [29], which indicates that a ferromagnetic phase sets in only if U ≥ U c (t 2 ), with t 2 being the next-nearest neighbor hopping amplitude. Müller et al studied one-and twodimensional Hubbard models with nearly-flat bands that are not in the class of Mielke and Tasaki flat-band models, since they do not obey some connectivity conditions [39].…”

“…This is indeed the case for the square lattice topological Hubbard model whose noninteracting limit is giving by the π-flux model [28]. As mentioned above, the spinwave spectrum [29] determined via exact diagonalization calculations for the flat-band ferromagnetic phase of the square lattice π-flux model in the (completely) flat-band limit qualitatively agrees with the harmonic one calculated within the bosonization formalism. Additional results for the square lattice π-flux model derived within the bosonization scheme are presented in Appendix C.…”

“…For the corresponding correlated Chern insulator, it was shown that the spin-wave spectrum has one gapped excitation branch and one gapless one, with the Goldstone mode at the centre of the first Brillouin zone. These analytical results qualitatively agrees with the numerical ones determined via exact diagonalization [29].…”

“…Correlation effects in a spinfull topological Hubbard model on a square lattice with nearly-flat noninteracting bands but at a commensurate filling were also discussed [27][28][29]. Here the noninteracting limit of the topological Hubbard model is given by the π-flux model, whose parameters can be adjusted such that the band structure is given by two lower and two higher (doubly degenerated) nearly-flat bands separated by an energy gap [22].…”

“…Here the noninteracting limit of the topological Hubbard model is given by the π-flux model, whose parameters can be adjusted such that the band structure is given by two lower and two higher (doubly degenerated) nearly-flat bands separated by an energy gap [22]. At 1/4-filling (half-filling of the lower band), it was shown [27][28][29] that such topological Hubbard model can realize a flat-band ferromagnetic phase [30]. In particular, one of us calculated the spin-wave excitation spectrum of the flat-band ferromagnetic phase within a bosonization formalism [28].…”