SPECTRAL PROPERTIES OF THE 2-DIMENSIONAL HUBBARD-MODEL

The self-energy of the hole-doped two-dimensional 2D Hubbard model is calculated to second order in the interaction U and the ensuing renorm alization of the spectral properties and of the Fermi surface is discu ssed. In uncorrelated systems the square-shaped Fermi surface separate s the Fermi surface closed around the Gamma point (with more holes tha n particles) from the Fermi surface closed around the Z point (with mo re particles than holes). In a correlated system a topological change from a Fermi surface centered around the Gamma point to a Fermi surfac e closed around a Z point is induced, either by increasing the interac tion or by diminishing the concentration of holes. The shape of the re normalized spectral function A(p)(omega) is momentum dependent. Using A(p)(omega) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clea rly seen. At high energies and far away from the Fermi surface the spe ctra acquire an additional peak that describes excitations in the Hubb ard band. The dispersion in Hubbard bands is weaker along the Gamma-Z, than Gamma-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically s ingular but the singular weight is reduced with respect to the uncorre lated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obta ined by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.