Doping on the kagome lattice: A variational Monte-Carlo study of the $t-J$ model

We study doping on the Kagome lattice by exploring the $t-J$-model with variational Monte-Carlo. We use a number of Gutzwiller projected spin-liquid and valence bond-crystal states and compare their energies at several system-sizes. We find that introducing mobile holes drives the system away from the Spin-Liquid state proposed by Ran et al for the undoped system, towards a uniform state with zero-flux. On top of the uniform-state a VBC of the Hastings-type is formed for low doping. The results are compared to exact diagonalization on small clusters. This agrees well.