Projected-Wave-Function Study of the Spin-1/2Heisenberg Model on the Kagomé Lattice

We perform a Gutzwiller projected-wave-function study for the spin-$1/2$ Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low-energy physics is governed by four flavors of two-component Dirac fermions coupled to a $U(1)$ gauge field. These results are discussed in the context of recent experiments on ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$.