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 the Bethe-Salpeter equation in the random phase approximation, we map the $U-t'$ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.