Violation of the Fermi-liquid picture in two-dimensional systems owing to Van Hove singularities - art. no. 205105

We consider the two-dimensional t-t' Hubbard model with the Fermi level bei ng close to Van Hove singularities. The phase diagram of the model is discu ssed. Far from the quantum phase transition (QPT) into ferro- (antiferro-) magnetic states. the self-energy at the singularity points has a nearly lin ear energy dependence, the density of states being proportional to ln(3)\ e psilon \. in the quantum-disordered and quantum-critical regimes near the Q PT a scaling approach is used. At small energies the self-energy demonstrat es a powerlike behavior with the exponent changing from unity to zero in a narrow energy interval. Provided that the system is close to ferromagnetic instability which occurs at t'/t --> -1/2, the quasiparticle spectral weigh t has, instead of a narrow peak. a broad maximum and is nonmonotonous at sm all energies. The application of the results to cuprates is discussed.