| Popis: |
The properties of the Hubbard model in one and two dimensions with N D sites are studied in the weak coupling limit. The single-particle self-energy is calculated, at T =0, for finite N and U N , around the Fermi energy, ω F , and Fermi momentum, p F . For D =1, the limit N →∞ gives the imaginary part of the self-energy as Im Σ pF (ω F +ω)/ U 2 ∼|ω | for |ω|∼1/ N . In 2-D, at half-filing and for p F =(π, 0), the dominant contribution to the self-energy is estimated as Im Σ pF (ω F +ω)/ U 2 ∼|ω|ln|ω|. The p F =(π/2, π/2) point gives Im Σ pF (ω F +ω)/ U 2 ∼|ω |. Away from half-filling, the dominant contribution is Im Σ p F (ω F +ω)/ U 2 ∼|ω| 2 ln|ω|. The differences in the excitation spectra of the U =0 and U →0 models in one and two dimensions are investigated in the N →∞ limit. |
