Exact hole-induced resonating-valence-bonds in certain infinite U Hubbard models

We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond (RVB)-like correlations in the infinite U Hubbard model on a triangular cactus -- a tree-like variant of a kagome lattice. The result is generalized to t-J models with antiferromagnetic interactions. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice. The results can be generalized to SU(N) t-J models, where the hole motion induces resonating SU(N)-flavor singlets. We then speculate concerning possible topological and superconducting phases that can arise purely from the hole motion.