Quasiparticle anisotropy and pseudogap formation: A weak-coupling renormalization-group analysis

We calculate the self-energy at weak-coupling for the t-t′ Hubbard model within the one-loop functional RG approach. At van Hove (vH) band fillings the quasiparticle (qp) concept is found invalid at kF=(π, 0). At low temperature the qp weight along the Fermi surface continuously vanishes from a finite value at the zone diagonal towards the (π, 0) point. Away from vH band fillings the qp peak is formed inside a pseudogap of size Δ, and within a finite frequency window |ω|≪Δ around the Fermi energy the electronic self-energy has the conventional Fermi-liquid form. With increasing separation between Fermi level and vHs the spectral anomalies gradually disappear.