The motion of a single hole in the infinite U Hubbard model on a bipartite (e.g., square) lattice induces a fully polarized metallic ferromagnetism — the phenomenon known as Nagaoka’s ferromagnetism. However, various numerical calculations suggest that the motion of a single hole on a non-bipartite triangular lattice induces antiferromagnetism. In this talk, I will discuss various "counter-Nagaoka theorems” that illuminate the origin of such itinerant antiferromagnetism. I will first consider a t-J model on a triangular cactus — a tree-like variant of a kagome lattice and show that the motion of a single hole induces the nearest-neighbor resonating-valence-bond (RVB)-like correlations. Then, I will discuss the generalization of such results to SU(N) t-J models. I will then discuss the possibility of topological and superconducting phases that can arise purely from the hole motion. Time permitted, I will talk about the exotic mechanism for metallic ferromagnetism induced by the quasi-one-dimensional mobility.
