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We report the results of a Hartree-Fock study applied to interactingelectrons moving in two different bipartite lattices: the dice and the Lieblattices, at half-filling. Both lattices develop ferrimagnetic order in thephase diagram $U$-$\lambda$, where $U$ is the Hubbard onsite repulsion and$\lambda$ the Rashba spin-orbit coupling strength. Our main result is theobservation of an unexpected multitude of topological phases for both lattices.All these phases are ferrimagnetic, but they differ among themselves in theirset of six Chern numbers (six numbers because the unit cells have three atoms).The Chern numbers $|C|$ observed in our study range from 0 to 3, showing thatlarge Chern numbers can be obtained by the effect of electronic correlations,adding to the recently discussed methodologies to increase $|C|$ based onextending the hopping range in tight-binding models, using sudden quenches, orphotonic crystals, all without including electronic interactions.

Multitude of Topological Phase Transitions in Bipartite Dice and Lieb Lattices with Interacting Electrons and Rashba Coupling