  We investigate the transition to the insulating state in the one-dimensional
Hubbard model with bond-charge interaction x (Hirsch model), at half-filling
and T=0. By means of the density-matrix renormalization group algorithm the
charge gap closure is examined by both standard finite size scaling analysis
and looking at singularities in the derivatives of single-site entanglement.
The results of the two techniques show that a quantum phase transition takes
place at a finite Coulomb interaction u_c(x) for x>0.5. The region 0<u<u_c
turns out to have a superconducting nature, at least for not too large x>x_c.
