The Hubbard model on the kagome lattice is presently often considered as a minimal model to describe the rich low-temperature behavior of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ compounds (with $A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$), 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 ferromagnetism 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 $A{\mathrm{V}}_3{\mathrm{Sb}}_5$. 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 $2\times 2$ periodicity, in closer agreement with experimental findings.

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• Charge density waves
• Electron-phonon coupling
• Van Hove singularity
• Kagome lattice
• Metals
• Hubbard model
• Lattice models in condensed matter
• Monte Carlo methods
• Variational approach