The Strong Coupling Limit of the Hubbard Model

We carry out a coordinated study of the two dimensional Hubbard model in the extreme strong-coupling limit, $\frac{U}{t}\to \infty $. The resulting problem has no parameters other than the mean electron concentration per site, n. As is well known, for n=1, the infinite U limit is singular, in that interactions of order$\frac{t^2}{U}$ must be included to resolve the $2^N$ fold degeneracy of the ground state found for infinite U. For any other value of n, however, the infinite U limit is well behaved, but incompletely understood. We have applied a combination of exact diaganolization and variational methods to explore the phase diagram of this paradigmatic model of strongly interacting electrons.