ANALYTIC PROPERTIES OF THE SELF-ENERGY OF THE HUBBARD-MODEL IN ONE AND 2 DIMENSIONS

A new method of calculating the properties of correlated electrons propagating on D-dimensional lattices with N(D) sites is used to study the analytic properties of the Hubbard model in one and two dimensions. The single-particle self-energy is evaluated in the weak-coupling limit around the Fermi energy, omega-F, and momentum, pF, at T = 0. For D = 1, the imaginary part of the self-energy, around pF and omega-F, behaves in the limit N --> infinity as Im SIGMA-pF(omega-F + omega) approximately \omega\ for \omega\ approximately 1/N. For D = 2 at half-filling and along the (1,0) direction in the Brillouin zone, the dominant contribution to the self-energy around omega-F is estimated as Im SIGMA-pF(omega-F + omega) approximately \omega\ 1n \omega\. For one and two dimensional lattices, the excitation spectra of the U = 0 and U --> 0 models become qualitatively different as N --> infinity and can not be simply connected by the perturbation theory.