Perturbation expansion for the two-dimensional Hubbard model - art. no. 035104

We develop an efficient method to calculate the third-order corrections to the self-energy of the hole-doped two-dimensional Hubbard model in space-ti me representation. Using the Dyson equation we evaluate the renormalized sp ectral function in various parts of the Brillouin zone and find significant modifications with respect to the second-order theory even for rather smal l values of the coupling constant U. The spectral function becomes unphysic al for U similar or equal toW where W is the half-width of the conduction b and. Close to the Fermi surface and for U<W, the single-particle spectral w eight is reduced in a finite energy interval around the Fermi energy. The i ncrease of U opens a gap between the occupied and unoccupied parts of the s pectral function.