  In this paper we report the latest results of exact diagonalizations of SU(2)
invariant models on various lattices (square, triangular, hexagonal,
checkerboard and kagome lattices). We focus on the low lying levels in each S
sector. The differences in behavior between gapless systems and gapped ones are
exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on
the kagome lattice is discussed. A rough estimate of the spin susceptibility in
such an hypothesis is given.The evolution of the intra-S channel spectra under
the effect of a small perturbation is consistent with the proximity of a
quantum critical point. We emphasize that the very small intra-S channel energy
scale observed in exact spectra is a very interesting information to understand
the low T dynamics of this model.
