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Magnons in multiorbital Hubbard models, from Lieb to kagome

We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using self-consistent Hartree-Fock approximation combined with real-time two-particle response functions from the Bethe-Salpeter equation in the random phase approximation, we map the $U-t'$ phase diagram of the Lieb-kagome lattices, identifying the typical magnetic states and the corresponding magnetic excitation spectra. In addition to gapless Goldstone magnons, the ferrimagnetic and antiferromagnetic symmetry-broken phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.