  When a van-Hove singularity is located in the vicinity of the Fermi level,
the electronic scattering rate acquires a non-analytic contribution. This
invalidates basic assumptions of Fermi liquid theory and within perturbative
treatments leads to a non-Fermi liquid self-energy and transport
properties.Such anomalies are shown to also occur in the strongly correlated
metallic state. We consider the Hubbard model on a two-dimensional square
lattice with nearest and next-nearest neighbor hopping within the single-site
dynamical mean-field theory. At temperatures on the order of the low-energy
scale $T_0$ an unusual maximum emerges in the imaginary part of the self-energy
which is renormalized towards the Fermi level for finite doping. At zero
temperature this double-well structure is suppressed, but an anomalous energy
dependence of the self-energy remains. For the frustrated Hubbard model on the
square lattice with next-nearest neighbor hopping, the presence of the van Hove
singularity changes the asymptotic low temperature behavior of the resistivity
from a Fermi liquid to non-Fermi liquid dependency as function of doping. The
results of this work are discussed regarding their relevance for
high-temperature cuprate superconductors.
