  We introduce a Hubbard model on a particular class of geometries, and
consider the effect of doping the highly spin-degenerate Mott-insulating state
with a microscopic number of holes in the extreme strong-coupling limit. The
geometry is quite general, with pairs of atomic sites at each superlattice
vertex, and a highly frustrated inter-atomic connectivity: the one dimensional
realization is a chain of edge-sharing tetrahedra. The sole model parameter is
the ratio of intra-pair to inter-pair hopping matrix elements. If the
intra-pair hopping is negligible then introducing a microscopic number of holes
results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair
hopping is comparable with the inter-pair hopping then the groundstate is low
spin with short-ranged spin correlations. We exactly solve the correlated
motion of a pair of holes in such a state and find that, in 1-d and 2-d, they
form a bound pair on a length scale that increases with diminishing binding
energy. This result is pertinent to the long-standing problem of hole motion in
the copper-oxide planes of the high-temperature superconductors: we have
rigorously shown that, on our frustrated geometry, the holes pair up and a
short-ranged low-spin state is generated by hole motion alone.

Strongly Correlated Electrons;Superconductivity