Hole Dynamics in the Two-Dimensional Strong-Coupling Hubbard Hamiltonian

Abstract

The effective Hamiltonian, obtained from the Hubbard model in the strong-coupling limit, is diagonalized exactly for a periodic two-dimensional square lattice of ten sites. We obtain the ground state of the system for any filling of the lattice and the K-space excitation spectrum for a single hole. Within our finite-size system, it is found that for very small coupling ratio t / U, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing t / U, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of t / U exists for which pairing of the holes may be possible.