Exact Hole-induced Resonating-Valence-Bond Ground State in Certain $U=\infty$ Hubbard Models

TL;DR

This paper proves that in certain $U=$ Hubbard models on a triangular cactus lattice, a single hole induces a nearest-neighbor resonating-valence-bond ground state, extending to related $t-J$ models with antiferromagnetic interactions.

Contribution

It establishes an exact ground state characterization for hole-doped Hubbard models on specific non-bipartite lattices, generalizing Nagaoka's theorem.

Findings

Single hole induces RVB ground state on triangular cactus lattice.

Results extend to $t-J$ models with $J  0$ on the same graphs.

Provides a weak converse to Nagaoka's theorem of ferromagnetism.

Abstract

We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond ground state in the $U=\infty$ Hubbard model on a triangular cactus - a tree-like variant of a kagome lattice. The result can be easily generalized to $t-J$ models with antiferromagnetic interactions $J\geq 0$ on the same graphs. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice.