Topological Magnons in a One-dimensional Itinerant Flat-Band Ferromagnet

Different from previous scenarios that topological magnons emerge in local spin models, we propose an alternative that itinerant magnets can host topological acoustic magnons. We consider a one-dimensional Tasaki model with a flat band, which can be viewed as a quarter filled periodic Anderson model with impurities locating at the center of the bonds and hybridizing with conducting electrons on their neighboring sites, together with a Hubbard repulsion for these electrons. By increasing this Hubbard interaction, the gap between the acoustic magnons and optical magnons closes and reopens while the Berry phase of the acoustic band changes from 0 to $\pi$, which leads to the occurrence of a topological transition. After this transition, consistent with the bulk-edge correspondence, there always exist in-gap edge magnon modes. The Hubbard interaction driven transition reveals a new mechanism to realize non-trivial magnon bands.