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The $S=1$ antiferromagnetic Heisenberg model on a Kagome lattice is studiedusing the density-matrix renormalization group method. To identify the groundstate, we take four kinds of clusters into account; periodic, cylindrical, andtwo open ones. The hexagonal singlet solid (HSS) and triangular valence bondsolid (TVBS) states are artificially generated by modulating edge shapes of theopen clusters. We find that the energy par sites of the HSS state is $e_0=E_0/N=-1.41095$, which is readily lower than that of the TVBS state ($e_0=-1.3912\pm 0.0025$). This agrees well with those of the cylindrical ($e_0=-1.40988$)and periodic ($e_0=-1.409 \pm 0.005$) clusters, where no assumption as to theordering is posed. Thus, we conclude that the HSS picture is consistent todescribe the ground state of the $S=1$ Kagome Heisenberg model. This is furtherconfirmed by finding non-symmetry-breaking state in the calculations of thedimer-dimer correlation functions as well as the entanglement entropy ofcylindrical clusters. Finally, we estimate the single-triplet energy gap: TheHSS ground state has $\Delta=0.1919$, while the TVBS excited state has a largerone $\Delta=0.2797$.

Non-Symmetry-Breaking Ground State of the S=1 Heisenberg Model on the Kagome lattice