Kagome Lattice Hubbard model at half filling

We investigate the Kagome lattice Hubbard model at half-filling by variational Monte-Carlo with testing the U(1)-Dirac spin liquid, uniform and valence bond crystal states. Even for the large-$U$ case the U(1) Dirac state, being the optimal state in the Heisenberg model, cannot be recovered. While the finite $U$ Hubbard model allows the introduction of vacancies in a different manner compared to the $t-J$ model, the physics appears to have many similarities. In particular a valence bond crystal is formed in the intermediate-$U$ regime. We observe an impact of the formation of this valence bond crystal on a possible Mott-transition in this model and discuss the properties of the wave-function.