On the violation of the Fermi-liquid picture in two-dimensional systems in the presence of van Hove singularities

We consider the two-dimensional t-t Hubbard model with the Fermi level being close to the van Hove singularities. The phase diagram of the model is discussed. In a broad energy region the self-energy at the singularity points has a nearly-linear energy dependence. The corresponding correction to the density of states is proportional to ln |ε|. Both realand imaginary part of the self-energy increase near the quantum phase transition into magnetically ordered or superconducting phase which implies violation of the Fermi-liquid behavior. The application of the results to cuprates is discussed. Typeset using REVTEX 1