Hole-hole correlations in the $U=\infty $ limit of the Hubbard model and the stability of the Nagaoka state

TL;DR

This study uses exact diagonalisation to analyze hole-hole correlations in the infinite-U Hubbard model, revealing that at higher densities, correlations resemble those of hard-core bosons, impacting the understanding of the Nagaoka state's stability.

Contribution

It provides a detailed comparison of multi-particle correlations in the infinite-U Hubbard model with those of spinless fermions and hard-core bosons, highlighting density-dependent behaviors.

Findings

Low hole densities favor a ferromagnetic fermionic description.

At larger densities, correlations resemble those of hard-core bosons.

Results inform the stability analysis of the Nagaoka state.

Abstract

We use exact diagonalisation in order to study the infinite - $U$ limit of the two dimensional Hubbard model. As well as looking at single-particle correlations, such as $n_{{\bf k}\sigma }=\langle c^\dagger _{{\bf k}\sigma }c_{{\bf k}\sigma } \rangle $, we also study {\it N-particle correlation functions} which compare the relative positions of {\it all} the particles in different models. In particular we study 16 and 18-site clusters and compare the charge correlations in the Hubbard model with those of spinless fermions and hard-core bosons. We find that although low densities of holes favour a `locally-ferromagnetic' fermionic description, the correlations at larger densities resemble those of pure hard-core bosons surprisingly well .