Pairing of holes in the Hubbard model

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Abstract
It is shown that a simple hole created in a singlet state of the strongly correlated Hubbard model, with one electron per atom, can substantially lower the kinetic energy of the system by binding to a spin fluctuation to form a magnetic polaron. Calculations are made for the linear chain, and for the square lattice which relates to the CuO2 layers in the new oxide superconductors. It is also shown that two simple holes can lower kinetic energy by binding to form a pair. The possibility is considered that two magnetic polarons, fermion-like with spin-1/2, may also lower kinetic energy by painting, thus leading to a type of superconductivity in which the normal state is not a Fermi liquid and where the transition temperature is determined by the bandwidth alone.