We consider the two-dimensional (formula presented) Hubbard model with the Fermi level being close to Van Hove singularities. The phase diagram of the model is discussed. Far from the quantum phase transition (QPT) into ferro- (antiferro-) magnetic states, the self-energy at the singularity points has a nearly linear energy dependence, the density of states being proportional to (formula presented) In the quantum-disordered and quantum-critical regimes near the QPT a scaling approach is used. At small energies the self-energy demonstrates 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 (formula presented) the quasiparticle spectral weight has, instead of a narrow peak, a broad maximum and is nonmonotonous at small energies. The application of the results to cuprates is discussed.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - 2001|