  We perform a Gutzwiller projected wavefunction study for the spin-1/2
Heisenberg model on the Kagome 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 ZnCu$_3$(OH)$_6$Cl$_2$.
