The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn$_3$Sn, Fe$_3$Sn$_2$, FeSn, Co$_3$Sn$_2$S$_2$, Gd$_3$Ru$_4$Al$_{12}$), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory (DMFT), the dynamical vertex approximation (D$Gamma$A), and determinant quantum Monte Carlo (DQMC). In contrast to the archetypal square-lattice, we find no tendencies towards magnetic ordering, as magnetic correlations remain short-range. Nevertheless, the magnetic correlations undergo a remarkable crossover as the system approaches the metal-to-insulator transition. The Mott transition itself does however not affect the magnetic correlations. Our equal-time and dynamical structure factors can be used as a reference for inelastic neutron scattering experiments on the growing family of metallic kagome materials.
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