  We report a two-step density-matrix renormalization-group computation of the
equal-time single-particle Green's function, the density-density correlations,
and the low-frequency spectral weight function of a spinless fermion model in
an anisotropic two-dimensional lattice at half-filling. We find that at weak
couplings the density-density correlations have the universal decay of a Fermi
liquid; the spectral weight function displays a sharp quasi-particle peak. But
in the vicinity of a quantum critical point, these correlations strongly
deviate from a Fermi liquid prediction and a pseudogap opens in the spectral
weight function.
