Hole dynamics in the two-dimensional strong-coupling Hubbard Hamiltonian

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 $\frac{t}{U}$, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing $\frac{t}{U}$, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of $\frac{t}{U}$ exists for which pairing of the holes may be possible.