  We study the energy and the static spin structure factor of the ground state
of the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome
lattice. By the iterative application of a few Lanczos steps on accurate
projected fermionic wave functions and the Green's function Monte Carlo
technique, we find that a gapless (algebraic) U(1) Dirac spin liquid is
competitive with previously proposed gapped (topological) Z2 spin liquids. By
performing a finite-size extrapolation of the ground-state energy, we obtain an
energy per site E/J=-0.4365(2), which is equal, within three error bars, to the
estimates given by the density-matrix renormalization group (DMRG). Our
estimate is obtained for a translationally invariant system, and, therefore,
does not suffer from boundary effects, like in DMRG. Moreover, on finite toric
clusters at the pure variational level, our energies are lower compared to
those from DMRG calculations.
