We present an extensive quantum Monte Carlo study of a nearest-neighbor, singlet-projection model on the kagome lattice that exhibits SO(N) symmetry and is sign-problem-free. We find that in contrast to the previously studied SU(N) variations of this model, the non-bipartite lattices appear to harbor spin-liquid phases for intermediate values of N, a result also seen on the triangular lattice with this same model. Unlike the triangular lattice, however, the kagome lattice appears to admit no valence bond solid (VBS) phase for large N, instead remaining a spin-liquid. We also observe that the spin-ordered phase survives to a relatively large value of N, at least N=8, and that it is gone for N=10; the fate of N=9 remains unclear.
@article{arxiv.1804.02824,
title = {SO($N$) singlet projection model on the kagome lattice},
author = {Matthew S. Block},
journal= {arXiv preprint arXiv:1804.02824},
year = {2018}
}