2024-12-2920242469-995010.1103/PhysRevB.109.0351492-s2.0-85183315090https://doi.org/10.1103/PhysRevB.109.035149https://hdl.handle.net/20.500.14288/22989We analyze the two -body spectrum within the Hofstadter-Hubbard model on a square lattice through an exact variational ansatz and study the topological properties of its low-lying two -body bound -state branches. In particular, we discuss how the Hofstadter-Hubbard butterfly of the two -body branches evolves as a function of onsite interactions and how to efficiently calculate their Chern numbers using the Fukui-Hatsugai-Suzuki approach. Our numerical results are fully consistent with the simple picture that appears in the strong -coupling limit, where the attraction between fermions forms a composite boson characterized by an effective hopping parameter and an effective magnetic -flux ratio. Materials sciencePhysics, appliedPhysics, condensed matterJournal article2469-9969 1173653700005Q241124