Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models

TL;DR

This paper proves that a single hole in certain $U=\infty$ $SU(N)$ Hubbard models induces $SU(N)$ flavor-singlets, suggesting possible antiferromagnetic or RVB-like polarons relevant for exotic phases and superconductivity.

Contribution

It generalizes the counter-Nagaoka theorem to $SU(N)$ models and demonstrates the formation of flavor-singlet polarons induced by holes on Husimi-like trees.

Findings

Single hole induces $SU(N)$ flavor-singlets in the model.

Results suggest existence of antiferromagnetic or RVB-like polarons.

Implications for strong-coupling superconductivity and exotic phases.

Abstract

We prove that the motion of a single hole induces $SU(N)$ flavor-singlets in the $U=\infty$ $SU(N)$ (Fermi) Hubbard model on a Husimi-like tree graph. The result is also generalized to certain $t$-$J$ models with antiferromagnetic interactions and singlet hopping terms typically neglected in the literature. This is an $SU(N)$ generalization of the "counter-Nagaoka theorem" introduced in [Phys. Rev. B 107, L140401 (2023)]. Our results suggest the existence of antiferromagnetic or resonating-valence-bond (RVB)-like polarons in the $t$-$J$ models on a more realistic non-bipartite lattice. Such antiferromagnetic/RVB polarons may be relevant for a novel strong-coupling mechanism of superconductivity or other exotic fractionalized phases of matter.