Dirac, Anderson, and Goldstone on the Kagome

Abstract

We show that there exists a long-range RVB state for the kagome 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 kagome lattice, including spin-Peierls solid and chiral spin liquid states. Using an RG 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 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.