Non-symmetry-breaking ground state of the S=1 Heisenberg model on the kagome lattice

The S = 1 antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is e(0) = E-0/(NJ) = -1.410 95, which is readily lower than that of the TVBS state (e(0) = -1.3912 +/- 0.0025). This agrees well with those of the cylindrical (e(0) = -1.4122) and periodic (e(0) = -1.4111) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the S = 1 kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has Delta/J = 0.178 +/- 0.005, whereas the higher TVBS state has a larger one Delta/J = 0.280.