| We consider the Hubbard model within the single-site dynamical mean-field theory (DMFT) on lattices which exhibit a van Hove singularity in the vicinity of the Fermi level. Analytical treatment of the lattice summation reveals a non-analytic contribution of the van Hove singularity to the local effective medium (Weiss field). This may leads to a non-Fermi liquid self-energy and transport properties within a full numerical solution of the DMFT on a two-dimensional square lattice with nearest- and next-nearest-neighbor hoppings. At temperatures on the order of the low-energy scale T0 an unusual maximum emerges in the imaginary part of the self-energy which is renormalized toward 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. The asymptotic low-temperature behavior of the resistivity changes from Fermi liquid to non-Fermi liquid behavior as function of doping. The results are also discussed regarding their relevance for quantum cluster approximations and high-temperature cuprate superconductors. |
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