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. [Y. Ran, M. Hermele, P. A. Lee, and X. G. Wen, Phys. Rev. Lett. 98, 117205 ( 2007)] for the undoped system, toward a uniform state with zero flux. On top of the uniform state a valence-bond crystal of the Hastings type is formed for low doping. The results are compared and agree well with exact diagonalization on small clusters.