  We apply the density-matrix renormalization group (DMRG) method to a
one-dimensional Hubbard model that lacks Umklapp scattering and thus provides
an ideal case to study the Mott-Hubbard transition analytically and
numerically. The model has a linear dispersion and displays a
metal-to-insulator transition when the Hubbard interaction~$U$ equals the band
width, $U_{\rm c}=W$, where the single-particle gap opens linearly,
$\Delta(U\geq W)=U-W$. The simple nature of the elementary excitations permits
to determine numerically with high accuracy the critical interaction strength
and the gap function in the thermodynamic limit. The jump discontinuity of the
momentum distribution $n_k$ at the Fermi wave number $k_{\rm F}=0$ cannot be
used to locate accurately $U_{\rm c}$ from finite-size systems. However, the
slope of $n_k$ at the band edges, $k_{\rm B}=\pm \pi$, reveals the formation of
a single-particle bound state which can be used to determine $U_{\rm c}$
reliably from $n_k$ using accurate finite-size data.
