Using the one-loop functional renormalization group technique we evaluate the self-energy in the weak-coupling regime of the 2D t-t′ Hubbard model. At van Hove (vH) band fillings and at low temperatures the quasiparticle weight along the Fermi surface (FS) continuously vanishes on approaching the (π,0) point where the quasiparticle concept is invalid. Away from vH band fillings the quasiparticle peak is formed inside an anisotropic pseudogap and the self-energy has the conventional Fermi-liquid characteristics near the Fermi level. The spectral weight of the quasiparticle features is reduced on parts of the FS between the near vicinity of hot spots and the FS points closest to (π,0) and (0,π).
- Antiferromagnetic fluctuations