The Hubbard model on the kagome lattice is presently often considered as a minimal model to describe the rich low-temperature behavior of AV3Sb5 compounds (with A = K, Rb, Cs), including charge density waves (CDWs), superconductivity, and possibly broken time-reversal symmetry. Here, we investigate, via variational Jastrow-Slater wave functions, the properties of its ground state when both on-site U and nearest-neighbor V Coulomb repulsions are considered at the van Hove filling. Our calculations reveal the presence of different interaction-driven CDWs and, contrary to previous renormalization-group studies, the absence of ferromag-netism and charge-or spin-bond order. No signatures of chiral phases are detected. Remarkably, the CDWs triggered by the nearest-neighbor repulsion possess charge disproportionations that are not compatible with the ones observed in AV3Sb5. As an alternative mechanism to stabilize charge-bond order, we consider the electron-phonon interaction, modeled by coupling the hopping amplitudes to quantum phonons, as in the Su-Schrieffer-Heeger model. Our results show the instability towards a trihexagonal distortion with 2 x 2 periodicity, in closer agreement with experimental findings.
