  Using the next-nearest neighbor (zig-zag) Hubbard chain as an one
dimemensional model, we investigate the influence of interactions on the
position of the Fermi wavevectors with the density-matrix renormalization-group
technique (DMRG). For suitable choices of the hopping parameters we observe
that electron-electron correlations induce very different renormalizations for
the two different Fermi wavevectors, which ultimately lead to a complete
destruction of one section of the Fermi sea in a quantum critical point.
