Dirac structure, RVB, and Goldstone modes in the kagomé antiferromagnet

We show that there exists a long-range resonating valence bond (RVB) state for the kagomé lattice spin-1/2 Heisenberg antiferromagnet for which the spinons have a massless Dirac spectrum. By considering various perturbations of the RVB state which give mass to the fermions by breaking a symmetry, we are able to describe a wide-ranging class of known states on the kagomé lattice, including spin-Peierls solid and chiral spin-liquid states. Using a renormalization group treatment of fluctuations about the RVB state, we propose yet a different symmetry breaking pattern and show how collective excitations about this state account for the gapless singlet modes seen experimentally and numerically. We make a further comparison with numerics for Chern numbers, dimer-dimer correlation functions, the triplet gap, and other quantities. To accomplish these calculations, we propose a variant of the SU(N) theory which enables us to include many of the effects of Gutzwiller projection at the mean-field level.