Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet

We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-1/2 quantum Heisenberg model on the kagome lattice. Starting from the algebraic U(1) Dirac spin liquid state proposed by Y. Ran {\it et al.} {Phys. Rev. Lett. {\bf 98}, 117205 (2007)}] and iteratively applying a few Lanczos steps, we compute the lowest S=2 excitation constructed by exciting spinons close to Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance spin-spin correlations in real space. The competition with a gapped (topological) spin liquid is discussed.