Gapless spin-liquid phases in the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice

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 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 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 errorbars, to the estimates given by density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant systems, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite clusters, our energies are systematically lower compared to those from DMRG calculations on a torus, and comparable to those on cylindrical geometries.