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

We use exact diagonalization 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(ksigma) = [c(ksigma)dagger c(ksigma)], we also study N-particle correlation functions, which compare the relative positions of 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 favor a ''locally ferromagnetic'' fermionic description, the correlations at larger densities resemble those of pure hard-core bosons surprisingly well.