The pinning of the Fermi level to the Van Hove singularity and the formation of flat bands in the two-dimensional $t-t^{\prime }$ Hubbard model is investigated by the renormalization group technique. The “Van Hove” scenario of non-Fermi-liquid behavior for high-$T_c$ compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on $\mathrm{L}{\mathrm{a}}_2\mathrm{C}\mathrm{u}{\mathrm{O}}_4$.

• Received 26 October 2001

DOI:https://doi.org/10.1103/PhysRevLett.89.076401