How correlations change the magnetic structure factor of the kagome Hubbard model

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., ${\mathrm{Mn}}_{3}\mathrm{Sn}, {\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$, FeSn, ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}, {\mathrm{Gd}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$, and $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ with $A=\mathrm{K}$, Rb, Cs), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory, the dynamical vertex approximation, and determinant quantum Monte Carlo. In contrast to the archetypal square lattice, we find no tendencies toward 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 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.