Triplet and singlet excitations in the valence bond crystal phase of the kagome lattice Heisenberg model

A proposed ground state for the kagome lattice Heisenberg model consists of a valence bond crystal (VBC) with a 36-site unit cell. We calculate the low-lying triplet and singlet excitations in the VBC phase for the infinite-lattice model and for the 36-site cluster. For the infinite lattice, the lowest triplet excitation is found to have a spin gap of approximately 0.08 +/- 0.02J and a bandwidth of only about 0.01J. For the 36-site cluster, which consists of a single unit cell with periodic boundary conditions, there are substantial finite-size effects: the spin gap there is estimated to be approximately 0.2J, which is close to the exact diagonalization result of 0.164J. The triplet excitations attract one another and form many bound states in the spin-singlet channel. We find a large number of such bound states for the 36-site cluster, many of which appear to lie below the spin gap, which is again in agreement with the results from exact diagonalization.