Low-Energy Singlets in the Heisenberg Antiferromagnet on the Kagome Lattice

The spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the kagome lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic $T^2$ specific heat observed experimentally.