Dimerization in the two-dimensional Hubbard model

We have used both an exact diagonalization method for finite-size systems and a perturbation technique to study the lattice instability due to dimerization in a two-dimensional Hubbard model in the large-U limit. We show that a critical electron-phonon coupling strength is required to form a dimerized state, in contrast to the 1-dimensional system. Our calculations suggest the phase transition to the dimerized state is of first order. The relevance to high-$T_c$ superconductor materials is discussed.