Numerical studies of the Hubbard model

Abstract

We have studied two problems. Firstly the density of hole states for the strongly correlated nearly half-filled Hubbard model on a d-dimensional hypercubic lattice was studied by the moment expansion method. Secondly, we studied the nearest-neighbour hopping Hubbard model in the atomic limit using high temperature series expansions for d=2 and d → ∞. For the first problem we found an essential singularity inside the band edges in the random and antiferromagnetic cases. For the second problem we found no evidence of a phase transition at any temperature greater than zero. © 1991.