Single-site entanglement at the superconductor-insulator transition in the Hirsch model

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 greater than or similar to 0.5. The region 0 < u < u(c) turns out to have a superconducting nature, at least for not too large x > x(c).