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A proposed ground state for the Kagome Lattice Heisenberg Model (KLHM)consists of a Valence Bond Crystal (VBC) with a 36-site unit cell. We calculatethe low-lying triplet and singlet excitations in the VBC phase for theinfinite-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$0.08 \pm 0.02 J$ and a bandwidth of only about $0.01 J$. For the 36-sitecluster, consisting of a single unit cell with periodic boundary conditions,there are substantial finite-size effects: the spin gap there is estimated tobe approximately $0.2 J$, close to the exact diagonalization result of $0.164J$. The triplet excitations attract one another and form many bound states inthe spin-singlet channel. We find a large number of such bound states for the36-site cluster, many of which appear to lie below the spin gap, again inagreement with the results from exact diagonalization.

Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model