Hole-hole correlations in the $U=\infty$ limit of the Hubbard model and the stability 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 $n_{\mathbf{k}\sigma }=⟨c_{\mathbf{k}\sigma }^{†}{c}_{\mathbf{k}\sigma }⟩$, 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 .

15 pages, REVTEX

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