Variational Monte-Carlo study of lightly doped kagome spin liquid

We study the t-J model on the Kagome lattice with small but non-zero doping by the large-scale variational Monte-Carlo simulation. We propose a new variational state which is equivalent to the U(1) quantum spin-liquid state proposed by Ying Ran at zero doping (Y. Ran, et al, Phys. Rev. Lett. 98, 117205 (2007)). Instead of a superconducting state, we show that the lowest energy state is a chiral Fermi liquid state with enlarged unit cell. By comparing this state with various types of projected spin-liquid states and valence bond crystal states, we find that our state has lower energy at small doping. The relation between this state and the holon Wigner crystal proposed by density-matrix renormalization group is also discussed.