Abstract
The two dimensional Hubbard model with repulsive interaction is studied in the tz. sbnd;matrixapproximation. At T = 0 the particle-particle correlation function and the tz. sbnd;matrix are obtained analytically so that it is shown that the tz. sbnd;matrix and hence the self-energy have no singularities in the upper half phase of the complex energy variable. The phase angle of the tz. sbnd;matrix δ(2 k F + q, ω), in the limit q→0 and ω→0, is found to depend on the ratio ω/q and is not always zero. This non-vanishing phase angle results in the logarithmic correction to the imaginary part of the self-energy as ImΣ( k F ,ϵ) ∝ ϵ 2 lm |ϵ|. However, the renormalization factor Z is finite at the Fermi surface suggesting that the stability of the Fermi liquid state at least within the conventional perturbation theory. The case of the attractive interaction has also been studied and the crossover from the Cooper pairing to the real-space pairing is indicated.
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